The complexity of weighted boolean #CSP*

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterized by a finite set F of nonnegative functions that may be used to assign weights to the configurations (feasible solutions) of a problem instance. Classical constraint satisfaction problems correspond to the special case of 0,1-valued functions. We show that computing the partition function, i.e., the sum of the weights of all configurations, is FP#P-complete unless either (1) every function in F is of “product type,” or (2) every function in F is “pure affine.” In the remaining cases, computing the partition function is in P

Exclusion statistics: A resolution of the problem of negative weights

We give a formulation of the single particle occupation probabilities for a system of identical particles obeying fractional exclusion statistics of Haldane. We first derive a set of constraints using an exactly solvable model which describes an ideal exclusion statistics system and deduce the general counting rules for occupancy of states obeyed by these particles. We show that the problem of negative probabilities may be avoided with these new counting rules.Comment: REVTEX 3.0, 14 page

Black hole state counting in loop quantum gravity

The two ways of counting microscopic states of black holes in the U(1) formulation of loop quantum gravity, one counting all allowed spin network labels j,m and the other only m labels, are discussed in some detail. The constraints on m are clarified and the map between the flux quantum numbers and m discussed. Configurations with |m|=j, which are sometimes sought after, are shown to be important only when large areas are involved. The discussion is extended to the SU(2) formulation.Comment: 5 page

Hardness of decoding quantum stabilizer codes

In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the decoding problem consists of determining the most likely recovery given the syndrome. The corresponding classical problem is known to be NP-complete, and a similar decoding problem for quantum codes is also known to be NP-complete. However, this decoding strategy is not optimal in the quantum setting as it does not take into account error degeneracy, which causes distinct errors to have the same effect on the code. Here, we show that optimal decoding of stabilizer codes is computationally much harder than optimal decoding of classical linear codes, it is #P

Multicellular rosettes drive fluid-solid transition in epithelial tissues

Models for confluent biological tissues often describe the network formed by cells as a triple-junction network, similar to foams. However, higher order vertices or multicellular rosettes are prevalent in developmental and {\it in vitro} processes and have been recognized as crucial in many important aspects of morphogenesis, disease, and physiology. In this work, we study the influence of rosettes on the mechanics of a confluent tissue. We find that the existence of rosettes in a tissue can greatly influence its rigidity. Using a generalized vertex model and effective medium theory we find a fluid-to-solid transition driven by rosette density and intracellular tensions. This transition exhibits several hallmarks of a second-order phase transition such as a growing correlation length and a universal critical scaling in the vicinity a critical point. Further, we elucidate the nature of rigidity transitions in dense biological tissues and other cellular structures using a generalized Maxwell constraint counting approach. This answers a long-standing puzzle of the origin of solidity in these systems.Comment: 11 pages, 5 figures + 8 pages, 7 figures in Appendix. To be appear in PR

Consistent Searches for SMEFT Effects in Non-Resonant Dijet Events

We investigate the bounds which can be placed on generic new-physics contributions to dijet production at the LHC using the framework of the Standard Model Effective Field Theory, deriving the first consistently-treated EFT bounds from non-resonant high-energy data. We recast an analysis searching for quark compositeness, equivalent to treating the SM with one higher-dimensional operator as a complete UV model. In order to reach consistent, model-independent EFT conclusions, it is necessary to truncate the EFT effects consistently at order $1/\Lambda^2$ and to include the possibility of multiple operators simultaneously contributing to the observables, neither of which has been done in previous searches of this nature. Furthermore, it is important to give consistent error estimates for the theoretical predictions of the signal model, particularly in the region of phase space where the probed energy is approaching the cutoff scale of the EFT. There are two linear combinations of operators which contribute to dijet production in the SMEFT with distinct angular behavior; we identify those linear combinations and determine the ability of LHC searches to constrain them simultaneously. Consistently treating the EFT generically leads to weakened bounds on new-physics parameters. These constraints will be a useful input to future global analyses in the SMEFT framework, and the techniques used here to consistently search for EFT effects are directly applicable to other off-resonance signals.Comment: v1: 23 pages, 9 figures, 3 tables; v2: references added, typos corrected, matches version published in JHE

Bit-Vector Model Counting using Statistical Estimation

Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms

Infrared singularities in Landau gauge Yang-Mills theory

We present a more detailed picture of the infrared regime of Landau gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered uniform scaling limit, when all external momenta tend to zero, also weaker kinematic divergences, when only some of the external momenta vanish. The second solution represents the recently proposed decoupling scenario where the gluons become massive and the ghosts remain bare. In this case we find that none of the vertex functions is enhanced, so that the infrared dynamics is entirely suppressed. Our analysis also provides a strict argument why the Landau gauge gluon dressing function cannot be infrared divergent.Comment: 29 pages, 25 figures; published versio