相关论文: Tap Complexity, the Cavity Method and Supersymmetr…

We introduce a definition of algorithmic symmetry able to capture essential aspects of geometric symmetry. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov-Chaitin complexity) of…

We study how the degree of symmetry in the couplings influences the performance of three mean field methods used for solving the direct and inverse problems for generalized Sherrington-Kirkpatrick models. In this context, the direct problem…

Topological complexity $\TC{B}$ of a space $B$ is introduced by M. Farber to measure how much complex the space is, which is first considered on a configuration space of a motion planning of a robot arm. We also consider a stronger version…

The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N-particle systems on a line for the case of separable center-of-mass motion. New decompositions of the superhamiltonian into…

This paper addresses biquadratic polynomial programming (BPP), an NP-hard optimization problem closely related to biquadratic tensors. We first establish several necessary and sufficient conditions for the positive semi-definiteness and…

We study possible effects of supersymmetry (SUSY) in CP asymmetries in non-leptonic $B_{d,s}$ decays in a variety of SUSY flavour models considered in literature. We use both mass insertion and vertex mixing methods to calculate…

A new viewpoint for the gauge hierarchy problem is proposed: compactification at a large scale, 1/R, leads to a low energy effective theory with supersymmetry softly broken at a much lower scale, \alpha/R. The hierarchy is induced by an…

One of the challenges of supersymmetry (SUSY) breaking and mediation is generating a mu term consistent with the requirements of electro-weak symmetry breaking. The most common approach to the problem is to generate the mu term through a…

We compute the supersymmetric (SUSY) contributions to the observables in Bs-->K+K- and Bs-->K0 anti-K0 decays. The hadronic parameters in the standard-model (SM) amplitudes are obtained from the Bd-->K0 anti-K0 decay using a recent approach…

The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…

A computational problem exhibits a "gap property" when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the…

We propose an iterative construction of solutions of the Thouless-Anderson-Palmer-equations for the Sherrington-Kirpatrick model. The iterative scheme is proved to converge exactly up to the de Almayda-Thouless-line. No results on the…

A novel realization of the gravity-mediated SUSY breaking is presented taking into account a continuous global R symmetry. Consistently with it, we employ a linear superpotential for the hidden sector superfield and a Kaehler potential…

The challenge in combined task and motion planning (TAMP) is the effective integration of a search over a combinatorial space, usually carried out by a task planner, and a search over a continuous configuration space, carried out by a…

We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:…

Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0 + 1)-dimensional N = 2 SUSY quantum mechanical (QM) model which is considered on…

Using the theory of negative association for measures and the notion of random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically…

Supersymmetry solves the gauge hierarchy problem of the Standard Model if the masses of supersymmetric partners of the SM particles are close to the weak scale. In this thesis, we argue that the supersymmetric Standard Model, while avoiding…

We develop an efficient technique to compute anomalies in supersymmetric theories by combining the so-called nonlocal regularization method and superspace techniques. To illustrate the method we apply it to a four dimensional toy model with…

Let $\mathrm{R}$ be a real closed field. We prove that for any fixed $d$, the equivariant rational cohomology groups of closed symmetric semi-algebraic subsets of $\mathrm{R}^k$ defined by polynomials of degrees bounded by $d$ vanishes in…