Tumor-infiltrating CCR2+ inflammatory monocytes counteract specific immunotherapy

Tumor development and progression is shaped by the tumor microenvironment (TME), a heterogeneous assembly of infiltrating and resident host cells, their secreted mediators and intercellular matrix. In this context, tumors are infiltrated by various immune cells with either pro-tumoral or anti-tumoral functions. Recently, we published our non-invasive immunization platform DIVA suitable as a therapeutic vaccination method, further optimized by repeated application (DIVA2). In our present work, we revealed the therapeutic effect of DIVA2 in an MC38 tumor model and specifically focused on the mechanisms induced in the TME after immunization. DIVA2 resulted in transient tumor control followed by an immune evasion phase within three weeks after the initial tumor inoculation. High-dimensional flow cytometry analysis and single-cell mRNA-sequencing of tumor-infiltrating leukocytes revealed cytotoxic CD8+ T cells as key players in the immune control phase. In the immune evasion phase, inflammatory CCR2+ PDL-1+ monocytes with immunosuppressive properties were recruited into the tumor leading to suppression of DIVA2-induced tumor-reactive T cells. Depletion of CCR2+ cells with specific antibodies resulted in prolonged survival revealing CCR2+ monocytes as important for tumor immune escape in the TME. In summary, the present work provides a platform for generating a strong antigen-specific primary and memory T cell immune response using the optimized transcutaneous immunization method DIVA2. This enables protection against tumors by therapeutic immune control of solid tumors and highlights the immunosuppressive influence of tumor infiltrating CCR2+ monocytes that need to be inactivated in addition for successful cancer immunotherapy.

Optimized dithranol-imiquimod-based transcutaneous immunization enables tumor rejection

Introduction

Transcutaneous immunization (TCI) is a non-invasive vaccination method promoting strong cellular immune responses, crucial for the immunological rejection of cancer. Previously, we reported on the combined application of the TLR7 agonist imiquimod (IMQ) together with the anti-psoriatic drug dithranol as novel TCI platform DIVA (dithranol/IMQ based vaccination). In extension of this work, we further optimized DIVA in terms of drug dose, application pattern and established a new IMQ formulation.

Methods

C57BL/6 mice were treated on the ear skin with dithranol and IMQ-containing ointments together with ovalbumin-derived peptides. T cell responses were determined by flow cytometry and IFN-ɤ ELISpot assay, local skin inflammation was characterized by ear swelling.

Results

Applying the adjuvants on separate skin sites, a reduced number of specific CD8+ T cells with effector function was detectable, indicating that the local concurrence of adjuvants and peptide antigens is required for optimal vaccination. Likewise, changing the order of dithranol and IMQ resulted in an increased skin inflammatory reaction, but lower frequencies of antigen-specific CD8+ T cells indicating that dithranol is essential for superior T cell priming upon DIVA. Dispersing nanocrystalline IMQ in a spreadable formulation (IMI-Sol+) facilitated storage and application rendering comparable immune responses. DIVA applied one or two weeks after the first immunization resulted in a massive increase in antigen-specific T cells and up to a ten-fold increased memory response. Finally, in a prophylactic tumor setting, double but no single DIVA treatment enabled complete control of tumor growth, resulting in full tumor protection.

Discussion

Taken together, the described optimized transcutaneous vaccination method leads to the generation of a strong cellular immune response enabling the effective control of tumor growth and has the potential for clinical development as a novel non-invasive vaccination method for peptide-based cancer vaccines in humans.

Cross-presenting Langerhans cells are required for the early reactivation of resident CD8+ memory T cells in the epidermis

Tissue-resident memory CD8+ T cells (TRM) reside at sites of previous infection, providing protection against reinfection with the same pathogen. In the skin, TRM patrol the epidermis, where keratinocytes are the entry site for many viral infections. Epidermal TRM react rapidly to cognate antigen encounter with the secretion of cytokines and differentiation into cytotoxic effector cells, constituting a first line of defense against skin reinfection. Despite the important protective role of skin TRM, it has remained unclear, whether their reactivation requires a professional antigen-presenting cell (APC). We show here, using a model system that allows antigen targeting selectively to keratinocytes in a defined area of the skin, that limited antigen expression by keratinocytes results in rapid, antigen-specific reactivation of skin TRM. Our data identify epidermal Langerhans cells that cross-present keratinocyte-derived antigens, as the professional APC indispensable for the early reactivation of TRM in the epidermal layer of the skin.

Metastate analysis of the ground states of two-dimensional Ising spin glasses

Using an efficient polynomial-time ground-state algorithm we investigate the Ising spin glass state at zero temperature in two dimensions. For large sizes, we show that the spin state in a central region is independent of the interactions far away, indicating a "single-state" picture, presumably the droplet model. Surprisingly, a single power law describes corrections to this result down to the smallest sizes studied.

Cutting-plane algorithms and solution whitening for the vertex-cover problem

The phase-transition behavior of the NP-hard vertex-cover (VC) combinatorial optimization problem is studied numerically by linear programming (LP) on ensembles of random graphs. As the basic Simplex (SX) algorithm suitable for such LPs may produce incomplete solutions for sufficiently complex graphs, the application of cutting-plane (CP) methods is sought. We consider Gomory and {0,1/2} cuts. We measure the probability of obtaining complete solutions with these approaches as a function of the average node degree c and observe transition between typically complete and incomplete phase regions. While not generally complete solutions are obtained for graphs of arbitrarily high complexity, the CP approaches still advance the boundary in comparison to the pure SX algorithm, beyond the known replica-symmetry breaking (RSB) transition at c=e≈2.718. In fact, our results provide evidence for another algorithmic transition at c≈2.90(2). Besides this, we quantify the transition between easy and hard solvability of the VC problem also in terms of numerical effort. Further we study the so-called whitening of the solution, which is a measure for the degree of freedom that single vertices experience with respect to degenerate solutions. Inspection of the quantities related to clusters of white vertices reveals that whitening is affected, only slightly but measurably, by the RSB transition.

Madecassic Acid—A New Scaffold for Highly Cytotoxic Agents

Due to their manifold biological activities, natural products such as triterpenoids have advanced to represent excellent leading structures for the development of new drugs. For this reason, we focused on the syntheses and cytotoxic evaluation of derivatives obtained from gypsogenin, hederagenin, and madecassic acid, cytotoxicity increased—by and large—from the parent compounds to their acetates. Another increase in cytotoxicity was observed for the acetylated amides (phenyl, benzyl, piperazinyl, and homopiperazinyl), but a superior cytotoxicity was observed for the corresponding rhodamine B conjugates derived from the (homo)-piperazinyl amides. In particular, a madecassic acid homopiperazinyl rhodamine B conjugate 24 held excellent cytotoxicity and selectivity for several human tumor cell lines. Thus, this compound was more than 10,000 times more cytotoxic than parent madecassic acid for A2780 ovarian cancer cells. We assume that the presence of an additional hydroxyl group at position C–6 in derivatives of madecassic, as well as the (2α, 3β) configuration of the acetates in ring A, had a beneficial effect onto the cytotoxicity of the conjugates, as well as onto tumor/non-tumor cell selectivity.

Density of Conjugated Antibody Determines the Extent of Fc Receptor Dependent Capture of Nanoparticles by Liver Sinusoidal Endothelial Cells

Despite considerable progress in the design of multifunctionalized nanoparticles (NPs) that selectively target specific cell types, their systemic application often results in unwanted liver accumulation. The exact mechanisms for this general observation are still unclear. Here we asked whether the number of cell-targeting antibodies per NP determines the extent of NP liver accumulation and also addressed the mechanisms by which antibody-coated NPs are retained in the liver. We used polysarcosine-based peptobrushes (PBs), which in an unmodified form remain in the circulation for >24 h due to the absence of a protein corona formation and low unspecific cell binding, and conjugated them with specific average numbers (2, 6, and 12) of antibodies specific for the dendritic cell (DC) surface receptor, DEC205. We assessed the time-dependent biodistribution of PB-antibody conjugates by in vivo imaging and flow cytometry. We observed that PB-antibody conjugates were trapped in the liver and that the extent of liver accumulation strongly increased with the number of attached antibodies. PB-antibody conjugates were selectively captured in the liver via Fc receptors (FcR) on liver sinusoidal endothelial cells, since systemic administration of FcR-blocking agents or the use of F(ab')₂ fragments prevented liver accumulation. Cumulatively, our study demonstrates that liver endothelial cells play a yet scarcely acknowledged role in liver entrapment of antibody-coated NPs and that low antibody numbers on NPs and the use of F(ab')₂ antibody fragments are both sufficient for cell type-specific targeting of secondary lymphoid organs and necessary to minimize unwanted liver accumulation.

Ordering behavior of the two-dimensional Ising spin glass with long-range correlated disorder

The standard short-range two-dimensional Ising spin glass is numerically well accessible, in particular, because there are polynomial-time ground-state algorithms. On the other hand, in contrast to higher dimensional spin glasses, it does not exhibit a rich behavior, i.e., no ordered phase at finite temperature. Here, we investigate whether long-range correlated bonds change this behavior. This would still keep the model numerically well accessible while exhibiting a more interesting behavior. The bonds are drawn from a Gaussian distribution with a two-point correlation for bonds at distance r that decays as (1+r^{2})^{-a/2}, a≥0. We study numerically with exact algorithms the ground-state and domain-wall excitations. Our results indicate that the inclusion of bond correlations still does not lead to a spin-glass order at any finite temperature. A further analysis reveals that bond correlations have a strong effect at local length scales, inducing ferro- and antiferromagnetic domains into the system. The length scale of ferro- and antiferromagnetic order diverges exponentially as the correlation exponent approaches a critical value, a→a_{crit}=0. Thus, our results suggest that the system becomes a ferro- or antiferromagnet only in the limit a→0.

The Anti-apoptotic Murine Cytomegalovirus Protein vMIA-m38.5 Induces Mast Cell Degranulation

Mast cells (MC) represent “inbetweeners” of the immune system in that they are part of innate immunity by acting as first-line sentinels for environmental antigens but also provide a link to adaptive immunity by secretion of chemokines that recruit CD8 T cells to organ sites of infection. An interrelationship between MC and cytomegalovirus (CMV) has been a blank area in science until recently when the murine model revealed a role for MC in the resolution of pulmonary infection by murine CMV (mCMV). As to the mechanism, MC were identified as a target cell type of mCMV. Infected MC degranulate and synthesize the CC-chemokine ligand-5 (CCL-5), which is released to attract protective virus-specific CD8 T cells to infected host tissue for confining and eventually resolving the productive, cytopathogenic infection. In a step forward in our understanding of how mCMV infection of MC triggers their degranulation, we document here a critical role for the mCMV m38.5 gene product, a mitochondria-localized inhibitor of apoptosis (vMIA). We show an involvement of mCMV vMIA-m38.5 in MC degranulation by two reciprocal approaches: first, by enhanced degranulation after m38.5 gene transfection of bone marrow-derived cell culture-grown MC (BMMC) and, second, by reduced degranulation of MC in peritoneal exudate cell populations infected ex corpore or in corpore with mutant virus mCMV-Δm38.5. These studies thus reveal a so far unknown function of mCMV vMIA-m38.5 and offer a previously unconsidered but biologically relevant cell system for further analyzing functional analogies between vMIAs of different CMV species.

Directed negative-weight percolation

We consider the negative-weight percolation model on directed graphs. In particular, we study the model on a two-dimensional, weighted, periodic, centered square lattice. Bond weights are taken from a distribution that allows for both positive and negative values. For a given realization of the disorder, a minimally weighted directed loop and path configuration is determined by performing a nontrivial transformation of the original lattice into a minimum-weight perfect matching problem. For this problem, fast polynomial-time algorithms are available, thus we could study large systems with high accuracy. Depending on the fraction of negatively and positively weighted bonds on the lattice, a continuous phase transition is identified and its characterizing critical exponents are estimated by means of a finite-size scaling analysis. We observe a strong change of the universality class with respect to standard directed percolation as well as with respect to undirected negative-weight percolation. Furthermore, the relation to directed polymers in random media is illustrated.

Transcutaneous immunization with CD40 ligation boosts cytotoxic T lymphocyte mediated antitumor immunity independent of CD4 helper cells in mice

Transcutaneous immunization (TCI) is a novel vaccination strategy that utilizes skin-associated lymphatic tissue to induce immune responses. Employing T-cell epitopes and the TLR7 agonist imiquimod onto intact skin mounts strong primary, but limited memory CTL responses. To overcome this limitation, we developed a novel imiquimod-containing vaccination platform (IMI-Sol) rendering superior primary CD8⁺ and CD4⁺ T-cell responses. However, it has been unclear whether IMI-Sol per se is restricted in terms of memory formation and tumor protection. In our present work, we demonstrate that the combined administration of IMI-Sol and CD40 ligation unleashes fullblown specific T-cell responses in the priming and memory phase, strongly enhancing antitumor protection in mice. Interestingly, these effects were entirely CD4⁺ T cell independent, bypassing the necessity of helper T cells. Moreover, blockade of CD70 in vivo abrogated the boosting effect of CD40 ligation, indicating that the adjuvant effect of CD40 in TCI is mediated via CD70 on professional APCs. Furthermore, this work highlights the so far underappreciated importance of the CD70/CD27 interaction as a promising adjuvant target in TCI. Summing up, we demonstrate that the novel formulation IMI-Sol represents a powerful vaccination platform when applied in combination with sufficient adjuvant thereby overcoming current limitations of TCI.

Mast cells within cellular networks

Mast cells are highly versatile in terms of their mode of activation by a host of stimuli and their ability to flexibly release a plethora of biologically highly active mediators. Within the immune system, mast cells can best be designated as an active nexus interlinking innate and adaptive immunity. Here we try to draw an arc from initiation of acute inflammatory reactions to microbial pathogens to development of adaptive immunity and allergies. This multifaceted nature of mast cells is made possible by interaction with multiple cell types of immunologic and nonimmunologic origin. Examples for the former include neutrophils, eosinophils, T cells, and professional antigen-presenting cells. These interactions allow mast cells to orchestrate inflammatory innate reactions and complex adaptive immunity, including the pathogenesis of allergies. Important partners of nonimmunologic origin include cells of the sensory neuronal system. The intimate association between mast cells and sensory nerve fibers allows bidirectional communication, leading to neurogenic inflammation. Evidence is accumulating that this mast cell/nerve crosstalk is of pathophysiologic relevance in patients with allergic diseases, such as asthma.

Distribution of diameters for Erdős-Rényi random graphs

We study the distribution of diameters d of Erdős-Rényi random graphs with average connectivity c. The diameter d is the maximum among all the shortest distances between pairs of nodes in a graph and an important quantity for all dynamic processes taking place on graphs. Here we study the distribution P(d) numerically for various values of c, in the nonpercolating and percolating regimes. Using large-deviation techniques, we are able to reach small probabilities like 10^{-100} which allow us to obtain the distribution over basically the full range of the support, for graphs up to N=1000 nodes. For values c<1, our results are in good agreement with analytical results, proving the reliability of our numerical approach. For c>1 the distribution is more complex and no complete analytical results are available. For this parameter range, P(d) exhibits an inflection point, which we found to be related to a structural change of the graphs. For all values of c, we determined the finite-size rate function Φ(d/N) and were able to extrapolate numerically to N→∞, indicating that the large-deviation principle holds.

9-Phenanthrol enhances the generation of an CD8+ T cell response following transcutaneous immunization with imiquimod in mice

BACKGROUND

Transcutaneous immunization (TCI) is a non-invasive vaccination strategy targeting the skin-associated lymphoid tissue. Topical application of the TLR7 agonist imiquimod as adjuvant in combination with peptide antigens activates the innate immune system and mounts cytotoxic T lymphocyte (CTL) responses.

OBJECTIVE

Based on the commercial 5% imiquimod-containing drug Aldara we aimed to develop an improved formulation with superior vaccination efficiencies. The primary target was the enhancement of mast cell activation as important key for the function of the innate immune system.

METHODS

We investigated the effects of 9-phenanthrol (9-phe) on the activation of mast cells in vitro and in vivo. For TCI, we applied 0.2% 9-phe in Aldara or Aldara alone as adjuvants in combination with the MHC class I - restricted peptide SIINFEKL. To monitor vaccination, mast cell degranulation, migration of DC and frequencies of epitope-specific CTL was assessed. In a transgenic tumor model, the efficiencies of prophylactic immunization against a tumor antigen were also monitored.

RESULTS

9-phe induced degranulation of mast cells in vitro and upon topical application in vivo. A mixture of 0.2% 9-phe in Aldara showed superior results regarding the migration of DC and the expansion of antigen-specific CTL. Consequently, prophylactic immunization with 0.2% 9-phe in Aldara caused enhanced protection against tumor inoculation.

CONCLUSION

Our data demonstrate that a simple modification of an adjuvant formulation can yield superior results in experimental vaccination protocols by boosting critical steps leading to the generation of an efficient CTL response.

Transcutaneous immunization with a novel imiquimod nanoemulsion induces superior T cell responses and virus protection

BACKGROUND

Transcutaneous immunization (TCI) is a novel vaccination strategy utilizing the skin associated lymphatic tissue to induce immune responses. TCI using a cytotoxic T lymphocyte (CTL) epitope and the Toll-like receptor 7 (TLR7) agonist imiquimod mounts strong CTL responses by activation and maturation of skin-derived dendritic cells (DCs) and their migration to lymph nodes. However, TCI based on the commercial formulation Aldara only induces transient CTL responses that needs further improvement for the induction of durable therapeutic immune responses.

OBJECTIVE

Therefore we aimed to develop a novel imiquimod solid nanoemulsion (IMI-Sol) for TCI with superior vaccination properties suited to induce high quality T cell responses for enhanced protection against infections.

METHODS

TCI was performed by applying a MHC class I or II restricted epitope along with IMI-Sol or Aldara (each containing 5% Imiquimod) on the shaved dorsum of C57BL/6, IL-1R, Myd88, Tlr7 or Ccr7 deficient mice. T cell responses as well as DC migration upon TCI were subsequently analyzed by flow cytometry. To determine in vivo efficacy of TCI induced immune responses, CTL responses and frequency of peptide specific T cells were evaluated on day 8 or 35 post vaccination and protection in a lymphocytic choriomeningitis virus (LCMV) infection model was assessed.

RESULTS

TCI with the imiquimod formulation IMI-Sol displayed equal skin penetration of imiquimod compared to Aldara, but elicited superior CD8⁺ as well as CD4⁺ T cell responses. The induction of T-cell responses induced by IMI-Sol TCI was dependent on the TLR7/MyD88 pathway and independent of IL-1R. IMI-Sol TCI activated skin-derived DCs in skin-draining lymph nodes more efficiently compared to Aldara leading to enhanced protection in a LCMV infection model.

CONCLUSION

Our data demonstrate that IMI-Sol TCI can overcome current limitations of previous imiquimod based TCI approaches opening new perspectives for transcutaneous vaccination strategies and allowing the use of this enhanced cutaneous drug-delivery system to be tailored for the improved prevention and treatment of infectious diseases and cancers.

Fragmentation properties of two-dimensional proximity graphs considering random failures and targeted attacks

The pivotal quality of proximity graphs is connectivity, i.e., all nodes in the graph are connected to one another either directly or via intermediate nodes. These types of graphs are often robust, i.e., they are able to function well even if they are subject to limited removal of elementary building blocks, as may occur for random failures or targeted attacks. Here, we study how the structure of these graphs is affected when nodes get removed successively until an extensive fraction is removed such that the graphs fragment. We study different types of proximity graphs for various node-removal strategies. We use different types of observables to monitor the fragmentation process, simple ones like the number and sizes of connected components and more complex ones like the hop diameter and the backup capacity, which is needed to make a network N-1 resilient. The actual fragmentation turns out to be described by a second-order phase transition. Using finite-size scaling analyses we numerically assess the threshold fraction of removed nodes, which is characteristic for the particular graph type and node deletion scheme; this suffices to decompose the underlying graphs.

Analysis of the phase transition in the two-dimensional Ising ferromagnet using a Lempel-Ziv string-parsing scheme and black-box data-compression utilities

In this work we consider information-theoretic observables to analyze short symbolic sequences, comprising time series that represent the orientation of a single spin in a two-dimensional (2D) Ising ferromagnet on a square lattice of size L(2)=128(2) for different system temperatures T. The latter were chosen from an interval enclosing the critical point T(c) of the model. At small temperatures the sequences are thus very regular; at high temperatures they are maximally random. In the vicinity of the critical point, nontrivial, long-range correlations appear. Here we implement estimators for the entropy rate, excess entropy (i.e., "complexity"), and multi-information. First, we implement a Lempel-Ziv string-parsing scheme, providing seemingly elaborate entropy rate and multi-information estimates and an approximate estimator for the excess entropy. Furthermore, we apply easy-to-use black-box data-compression utilities, providing approximate estimators only. For comparison and to yield results for benchmarking purposes, we implement the information-theoretic observables also based on the well-established M-block Shannon entropy, which is more tedious to apply compared to the first two "algorithmic" entropy estimation procedures. To test how well one can exploit the potential of such data-compression techniques, we aim at detecting the critical point of the 2D Ising ferromagnet. Among the above observables, the multi-information, which is known to exhibit an isolated peak at the critical point, is very easy to replicate by means of both efficient algorithmic entropy estimation procedures. Finally, we assess how good the various algorithmic entropy estimates compare to the more conventional block entropy estimates and illustrate a simple modification that yields enhanced results.

Biased and greedy random walks on two-dimensional lattices with quenched randomness: the greedy ant within a disordered environment

The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are "greedy" in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of "energy" for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρ(c), resulting from numerically exact and "static" simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.

Information-theoretic approach to ground-state phase transitions for two- and three-dimensional frustrated spin systems

The information-theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity), and multi-information are used to analyze ground-state spin configurations for disordered and frustrated model systems in two and three dimensions. For both model systems, ground-state spin configurations can be obtained in polynomial time via exact combinatorial optimization algorithms, which allowed us to study large systems with high numerical accuracy. Both model systems exhibit a continuous transition from an ordered to a disordered ground state as a model parameter is varied. By using the above information-theoretic observables it is possible to detect changes in the spatial structure of the ground states as the critical point is approached. It is further possible to quantify the scaling behavior of the information-theoretic observables in the vicinity of the critical point. For both model systems considered, the estimates of critical properties for the ground-state phase transitions are in good agreement with existing results reported in the literature.

Analysis of the loop length distribution for the negative-weight percolation problem in dimensions d=2 through d=6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in the full ensemble of loops with negative weight, i.e., nontrivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize-using this extensive and exhaustive numerical study-the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations, we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.

Numerical solution-space analysis of satisfiability problems

The solution-space structure of the three-satisfiability problem (3-SAT) is studied as a function of the control parameter α (ratio of the number of clauses to the number of variables) using numerical simulations. For this purpose one has to sample the solution space with uniform weight. It is shown here that standard stochastic local-search (SLS) algorithms like average satisfiability (ASAT) exhibit a sampling bias, as does "Metropolis-coupled Markov chain Monte Carlo" (MCMCMC) (also known as "parallel tempering") when run for feasible times. Nevertheless, unbiased samples of solutions can be obtained using the "ballistic-networking approach," which is introduced here. It is a generalization of "ballistic search" methods and yields also a cluster structure of the solution space. As application, solutions of 3-SAT instances are generated using ASAT plus ballistic networking. The numerical results are compatible with a previous analytical prediction of a simple solution-space structure for small values of α and a transition to a clustered phase at α(c)≈3.86 , where the solution space breaks up into several non-negligible clusters. Furthermore, in the thermodynamic limit there are, even for α=4.25 close to the SAT-UNSAT transition α(s)≈4.267 , always clusters without any frozen variables. This may explain why some SLS algorithms are able to solve very large 3-SAT instances close to the SAT-UNSAT transition.

Upper critical dimension of the negative-weight percolation problem

By means of numerical simulations, we investigate the geometric properties of loops on hypercubic lattice graphs in dimensions d=2 through 7, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of system-spanning loops of total negative weight. The resulting negative-weight percolation (NWP) problem is fundamentally different from conventional percolation, as we have seen in previous studies of this model for the two-dimensional case. Here, we characterize the transition for hypercubic systems, where the aim of the present study is to get a grip on the upper critical dimension d u of the NWP problem. For the numerical simulations, we employ a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. We characterize the loops via observables similar to those in percolation theory and perform finite-size scaling analyses, e.g., three-dimensional hypercubic systems with side length up to L=56 sites, in order to estimate the critical properties of the NWP phenomenon. We find our numerical results consistent with an upper critical dimension d u=6 for the NWP problem.

Minimum-free-energy distribution of RNA secondary structures: Entropic and thermodynamic properties of rare events

We study the distribution of the minimum free energy (MFE) for the Turner model of pseudoknot free RNA secondary structures over ensembles of random RNA sequences. In particular, we are interested in those rare and intermediate events of unexpected low MFEs. Generalized ensemble Markov-chain Monte Carlo methods allow us to explore the rare-event tail of the MFE distribution down to probabilities such as 10^{-70} and to study the relationship between the sequence entropy and structural properties for sequence ensembles with fixed MFEs. Entropic and structural properties of those ensembles are compared with natural RNA of the same reduced MFE ( z score).

Finite-temperature local protein sequence alignment: percolation and free-energy distribution

Sequence alignment is a tool in bioinformatics that is used to find homological relationships in large molecular databases. It can be mapped on the physical model of directed polymers in random media. We consider the finite-temperature version of local sequence alignment for proteins and study the transition between the linear phase and the biologically relevant logarithmic phase, where the free energy grows linearly or logarithmically with the sequence length. By means of numerical simulations and finite-size-scaling analysis, we determine the phase diagram in the plane that is spanned by the gap costs and the temperature. We use the most frequently used parameter set for protein alignment. The critical exponents that describe the parameter-driven transition are found to be explicitly temperature dependent. Furthermore, we study the shape of the (free-) energy distribution close to the transition by rare-event simulations down to probabilities on the order 10(-64). It is well known that in the logarithmic region, the optimal score distribution (T=0) is described by a modified Gumbel distribution. We confirm that this also applies for the free-energy distribution (T>0). However, in the linear phase, the distribution crosses over to a modified Gaussian distribution.

Phase transitions in diluted negative-weight percolation models

We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of total negative weight. The resulting percolation problem is fundamentally different from conventional percolation, as we have seen in a previous study of this model for the undiluted case. Here, we investigate how the percolation transition is affected by additional dilution. We consider two types of dilution: either a certain fraction of edges exhibits zero weight, or a fraction of edges is even absent. We study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms. We perform a finite-size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary. We find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change in the universality class.

Conformal invariance and stochastic Loewner evolution processes in two-dimensional Ising spin glasses

We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with kappa approximately 2.1. An argument is given that their fractal dimension d(f) is related to their interface energy exponent theta by d(f) - 1 = 3/[4(3 + theta)], which is consistent with the commonly quoted values d(f) approximately 1.27 and theta approximately -0.28.

Calculation of partition functions by measuring component distributions

A new algorithm is presented, which allows us to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g., Ising models or Potts models (for arbitrary values q>0), including random or diluted models. The new approach is suitable for large systems. The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the case of zero degrees of freedom, where the exact result Z=1 is known. As an application, d=2 and d=3 dimensional ferromagnetic Potts models are studied, and the critical values qc, where the transition changes from second to first order, are determined. Large systems of sizes N=1000(2) and N=100(3) are treated. The critical value qc(d=2)=4 is confirmed and qc(d=3)=2.35(5) is found.

Corrections to scaling are large for droplets in two-dimensional spin glasses

The energy of a droplet of linear extent l in the droplet theory of spin glasses goes as l(theta) for large l. It is shown by numerical studies of large droplets in two-dimensional systems that this formula needs to be modified by the addition of a scaling correction l(-omega) in order to accurately describe droplet energies at the length scales currently probed in numerical simulations. Using this simple modification, it is now possible to explain many results which have been found in simulations of three-dimensional Ising spin glasses with the droplet model.

Hiding solutions in random satisfiability problems: a statistical mechanics approach

A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of statistical mechanics results, we propose random generators of hard and satisfiable instances for the 3-satisfiability problem. The design of the hardest problem instances is based on the existence of a first order ferromagnetic phase transition and the glassy nature of excited states. The analytical predictions are corroborated by numerical results obtained from complete as well as stochastic local algorithms.

Stress relaxation of near-critical gels

The time-dependent stress relaxation for a Rouse model of a cross-linked polymer melt is completely determined by the spectrum of eigenvalues of the connectivity matrix. The latter has been computed analytically for a mean-field distribution of cross-links. It shows a Lifshitz tail for small eigenvalues and all concentrations below the percolation threshold, giving rise to a stretched exponential decay of the stress relaxation function in the sol phase. At the critical point the density of states is finite for small eigenvalues, resulting in a logarithmic divergence of the viscosity and an algebraic decay of the stress relaxation function. Numerical diagonalization of the connectivity matrix supports the analytical findings and has furthermore been applied to cluster statistics corresponding to random bond percolation in two and three dimensions.

Minimal vertex covers on finite-connectivity random graphs: a hard-sphere lattice-gas picture

The minimal vertex-cover (or maximal independent-set) problem is studied on random graphs of finite connectivity. Analytical results are obtained by a mapping to a lattice gas of hard spheres of (chemical) radius 1, and they are found to be in excellent agreement with numerical simulations. We give a detailed description of the replica-symmetric phase, including the size and entropy of the minimal vertex covers, and the structure of the unfrozen component which is found to percolate at a connectivity c approximately 1.43. The replica-symmetric solution breaks down at c=e approximately 2.72. We give a simple one-step replica-symmetry-broken solution, and discuss the problems in the interpretation and generalization of this solution.

Spin domains generate hierarchical ground state structure in J = +/-1 spin glasses

Unbiased samples of ground states were generated for the short-range Ising spin glass with J(ij) = +/-1, in three dimensions. Clustering the ground states revealed their hierarchical structure, which is explained by correlated spin domains, serving as cores for macroscopic zero energy "excitations."

Typical solution time for a vertex-covering algorithm on finite-connectivity random graphs

We analytically describe the typical solution time needed by a backtracking algorithm to solve the vertex-cover problem on finite-connectivity random graphs. We find two different transitions: The first one is algorithm dependent and marks the dynamical transition from linear to exponential solution times. The second one gives the maximum computational complexity, and is found exactly at the threshold where the system undergoes an algorithm-independent phase transition in its solvability. Analytical results are corroborated by numerical simulations.

Ground-state clusters of two-, three-, and four-dimensional +/-J Ising spin glasses

A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +/-J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20(2),8(3),6(4) spins are treated. A "ballistic-search" algorithm is applied, which allows even for large system sizes to identify clusters of ground states that are connected by chains of zero-energy flips of spins. The number of clusters n(C) diverges with N going to infinity. For all dimensions considered here, an exponential increase of n(C) appears to be more likely than a growth with a power of N. The number of different ground states is found to grow clearly exponentially with N. A zero-temperature entropy per spin of s(0)=0.078(5)k(B) (2D), s(0)=0.051(3)k(B) (3D), respectively, s(0)=0.027(5)k(B) (4D) is obtained.

Number of guards needed by a museum: a phase transition in vertex covering of random graphs

In this Letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This transition is characterized by means of exact numerical simulations as well as by analytical replica calculations. The replica symmetric phase diagram is in excellent agreement with numerical findings up to average connectivity e, where replica symmetry becomes locally unstable.

Calculation of ground states of four-dimensional +/-J Ising spin glasses

Ground states of four-dimensional (d=4) Edwards-Anderson Ising spin glasses are calculated for sizes up to 7 x 7 x 7 x 7 using a combination of a genetic algorithm and cluster-exact approximation. The ground-state energy of the infinite system is extrapolated as e0(infinity)=-2.095(1). The ground-state stiffness (or domain wall) energy Delta is calculated. A delta approximately L(theta(S)) behavior with theta(S)=0.64(5) is found which confirms that the d=4 model has an equilibrium spin-glass-paramagnet transition for nonzero T(c).