Zeta functions of the 3-dimensional almost-Bieberbach groups

The subgroup zeta function and the normal zeta function of a finitely generated virtually nilpotent group can be expressed as finite sums of Dirichlet series admitting Euler product factorization. We compute these series except for a finite number of local factors when the group is virtually nilpotent of Hirsch length 3. We deduce that they can be meromorphically continued to the whole complex plane and that they satisfy local functional equations. The complete computation (with no exception of local factors) is presented for those groups that are also torsion-free, that is, for the 3-dimensional almost-Bieberbach groups.

An Energy Efficient UAV-Based Edge Computing System with Reliability Guarantee for Mobile Ground Nodes

An edge computing system is a distributed computing framework that provides execution resources such as computation and storage for applications involving networking close to the end nodes. An unmanned aerial vehicle (UAV)-aided edge computing system can provide a flexible configuration for mobile ground nodes (MGN). However, edge computing systems still require higher guaranteed reliability for computational task completion and more efficient energy management before their widespread usage. To solve these problems, we propose an energy efficient UAV-based edge computing system with energy harvesting capability. In this system, the MGN makes requests for computing service from multiple UAVs, and geographically proximate UAVs determine whether or not to conduct the data processing in a distributed manner. To minimize the energy consumption of UAVs while maintaining a guaranteed level of reliability for task completion, we propose a stochastic game model with constraints for our proposed system. We apply a best response algorithm to obtain a multi-policy constrained Nash equilibrium. The results show that our system can achieve an improved life cycle compared to the individual computing scheme while maintaining a sufficient successful complete computation probability.

Towards a complete mass spectrum of type-IIB flux vacua at large complex structure

The large number of moduli fields arising in a generic string theory compactification makes a complete computation of the low energy effective theory infeasible. A common strategy to solve this problem is to consider Calabi-Yau manifolds with discrete symmetries, which effectively reduce the number of moduli and make the computation of the truncated Effective Field Theory possible. In this approach, however, the couplings (e.g., the masses) of the truncated fields are left undetermined. In the present paper we discuss the tree-level mass spectrum of type-IIB flux compactifications at Large Complex Structure, focusing on models with a reduced one-dimensional complex structure sector. We compute the tree-level spectrum for the dilaton and complex structure moduli, including the truncated fields, which can be expressed entirely in terms of the known couplings of the reduced theory. We show that the masses of this set of fields are naturally heavy at vacua consistent with the KKLT construction, and we discuss other phenomenologically interesting scenarios where the spectrum involves fields much lighter than the gravitino. We also derive the probability distribution for the masses on the ensemble of flux vacua, and show that it exhibits universal features independent of the details of the compactification. We check our results on a large sample of flux vacua constructed in an orientifold of the Calabi-Yau $$ {\mathbbm{W}\mathrm{\mathbb{P}}}_{\left[1,1,1,1,4\right]}^4 $$ W ℙ 1 1 1 1 4 4 . Finally, we also discuss the conditions under which the spectrum derived here could arise in more general compactifications.

Comparative analysis of one-time hash-based signatures

Hash-based signatures are a wide class of post-quantum cryptographic algorithms, their security is based on the complexity of collision and preimage search problems for cryptographic hash functions. The main advantages of this class are post-quantization, easy modification and a well-researched mathematical base. The disadvantages are large sizes of signatures and limited number of uses of one key pair. The most promising algorithms of this class include algorithms of the SPHINCS type, which have a complex structure, including, among others, a one-time Winternitz signature. The paper analyzes the existing one-time signature algorithms, both well-known Lamport and Winternitz schemes, taking into account modifications of the latter one, and alternative methods. An analysis of the security of modified algorithms has been shown, which showed that their security is based on the same mathematical basis as the security of the original algorithms. The one-time use requirement remains critical to the safety of each of the algorithms studied. The sizes of keys and signatures and computational complexity of various algorithms are compared, in what their basic differences consist. The modified algorithms do not add fundamentally new components in cryptosystems but they make it possible to achieve a certain optimization, shifting the conditions of space-time compromise. The extended Lamport signature is of a particular interest, having the same computational complexity and key sizes as the original algorithm, and at the same time allowing one to halve the signature size. In the context of the SPHINCS cryptosystem, the Winternitz signature remains the best option, since it allows the complete computation of the public key directly from the signature.

Symmetry resolved entanglement in integrable field theories via form factor bootstrap

We consider the form factor bootstrap approach of integrable field theories to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are determined in an intuitive way and their solution is presented for the massive Ising field theory and for the genuinely interacting sinh-Gordon model, both possessing a ℤ2 symmetry. The solutions are carefully cross-checked by performing various limits and by the application of the ∆-theorem. The issue of symmetry resolution for discrete symmetries is also discussed. We show that entanglement equipartition is generically expected and we identify the first subleading term (in the UV cutoff) breaking it. We also present the complete computation of the symmetry resolved von Neumann entropy for an interval in the ground state of the paramagnetic phase of the Ising model. In particular, we compute the universal functions entering in the charged and symmetry resolved entanglement.

Fixed poin sets in digital topology, 1

<p>In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results that often differ greatly from standard results in classical topology.</p><p>We introduce several measures related to fixed points for continuous self-maps on digital images, and study their properties. Perhaps the most important of these is the fixed point spectrum F(X) of a digital image: that is, the set of all numbers that can appear as the number of fixed points for some continuous self-map. We give a complete computation of F(C_n) where C_n is the digital cycle of n points. For other digital images, we show that, if X has at least 4 points, then F(X) always contains the numbers 0, 1, 2, 3, and the cardinality of X. We give several examples, including C_n, in which F(X) does not equal {0, 1, . . . , #X}.</p><p>We examine how fixed point sets are affected by rigidity, retraction, deformation retraction, and the formation of wedges and Cartesian products. We also study how fixed point sets in digital images can be arranged; e.g., for some digital images the fixed point set is always connected.</p>

Digitalizing 360 Degree Employee Competency using Banzhaf Power Index and CDF

Traditionally, 360 degree evaluation of employee competency has been done using ratings given by Subordinates or Direct Reports, Peers, Manager and Self. Based on the rating by all rating group, the competency of the employee is determined. The gap between self-rating and ratings of all other group determines whether an employee has hidden strength or has blind spot in each competency variable. However, whenever larger number of subordinates or peers rates an employee, there is inherent bias and the employee’s overall competency rating can be low if the larger group holds grudge against the employee. To avoid bias and determine true rating, this paper proposes innovative use of Banzhaf Power Index. The complete computation and digitalization of Banzhaf Power Index for Chennai based Wind Energy Company is carried out and presented in this paper. The interactive Wolfram Computable Document Format (CDF) has also been created for wider use by personnel managers of other companies.

The Concept of Geodetic Analyses of the Measurement Results Obtained by Hydrostatic Leveling

The article discusses the issue of hydrostatic leveling. Its application is presented in structural health monitoring systems in order to determine vertical displacements of controlled points. Moreover, the article includes a complete computation scheme that utilizes the estimation from observation differences, allowing the elimination of the influence of individual sensors’ systematic errors. The authors suggest two concepts of processing the measurement results depending on the sensors’ connection method. Additionally, the second concept is extended by the elements allowing the prediction of the displacements by means of Kalman filtering.

The BNSR-invariants of the Houghton groups, concluded

We give a complete computation of the Bieri–Neumann–Strebel–Renz invariants Σm(Hn) of the Houghton groups Hn. Partial results were previously obtained by the author, with a conjecture about the full picture, which we now confirm. The proof involves covering relevant subcomplexes of an associated CAT (0) cube complex by their intersections with certain locally convex subcomplexes, and then applying a strong form of the Nerve Lemma. A consequence of the full computation is that for each 1 ≤ m ≤ n − 1, Hn admits a map onto ℤ whose kernel is of type Fm−1 but not Fm; moreover, no such kernel is ever of type Fn−1.