arXiv subjects

Eugene Perevalov

Publications and source records attributed to Eugene Perevalov.

13 recordsLinked to original sources

arXiv2022

Route Discovery and Capacity of Ad hoc Networks

Throughput capacity of large ad hoc networks has been shown to scale adversely with the size of network $n$. However the need for the nodes to find or repair routes has not been analyzed in this context. In this paper, we explicitly take route discovery into account and obtain the scaling law for the throughput capacity under general assumptions on the network environment, node behavior, and the quality of route discovery algorithms. We also discuss a number of possible scenarios and show that the need for route discovery may change the scaling for the throughput capacity dramatically.

cs.NI↗

arXiv2013

Towards the full information chain theory: question difficulty

A general problem of optimal information acquisition for its use in decision making problems is considered. This motivates the need for developing quantitative measures of information sources' capabilities for supplying accurate information depending on the particular content of the latter. In this article, the notion of a real valued difficulty functional for questions identified with partitions of problem parameter space is introduced and the overall form of this functional is derived that satisfies a particular system of reasonable postulates. It is found that, in an isotropic case, the resulting difficulty functional depends on a single scalar function on the parameter space that can be interpreted -- using parallels with classical thermodynamics -- as a temperature-like quantity, with the question difficulty itself playing the role of thermal energy. Quantitative relationships between difficulty functionals of different questions are also explored.

physics.data-an↗

arXiv2013

Towards the full information chain theory: answer depth and source models

A problem of optimal information acquisition for its use in general decision making problems is considered. This motivates the need for developing quantitative measures of information sources' capabilities for supplying accurate information depending on the particular content of the latter. A companion article developed the notion of a question difficulty functional for questions concerning input data for a decision making problem. Here, answers which an information source may provide in response to such questions are considered. In particular, a real valued answer depth functional measuring the degree of accuracy of such answers is introduced and its overall form is derived under the assumption of isotropic knowledge structure of the information source. Additionally, information source models that relate answer depth to question difficulty are discussed. It turns out to be possible to introduce a notion of an information source capacity as the highest value of the answer depth the source is capable of providing.

physics.data-an↗

arXiv2013

Towards the full information chain theory: solution methods for optimal information acquisition problem

When additional information sources are available in decision making problems that allow stochastic optimization formulations, an important question is how to optimally use the information the sources are capable of providing. A framework that relates information accuracy determined by the source's knowledge structure to its relevance determined by the problem being solved was proposed in a companion paper. There, the problem of optimal information acquisition was formulated as that of minimization of the expected loss of the solution subject to constraints dictated by the information source knowledge structure and depth. Approximate solution methods for this problem are developed making use of probability metrics method and its application for scenario reduction in stochastic optimization.

physics.data-an↗

arXiv2013

Information-related complexity: a problem-oriented approach

A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success. The complexity is defined as the minimum (quasi-)quantity of information that's necessary to complete the task to the given extent -- measured by the corresponding loss. The complexity so defined is shown to generalize the existing notion of statistical complexity when the system in question can be described by a discrete-time stochastic process. The proposed definition also applies, in particular, to optimization and decision making problems under uncertainty in which case it gives the agent a useful measure of the problem's "susceptibility" to additional information and allows for an estimation of the potential value of the latter.

physics.data-an↗

arXiv2013

Towards the full information chain theory: expected loss and information relevance

When additional information sources are available, an important question for an agent solving a certain problem is how to optimally use the information the sources are capable of providing. A framework that relates information accuracy on the source side to information relevance on the problem side is proposed. An optimal information acquisition problem is formulated as that of question selection to maximize the loss reduction for the problem solved by the agent. A duality relationship between pseudoenergy (accuracy related) quantities on the source side and loss (relevance related) quantities on the problem side is observed.

physics.data-an↗

arXiv1999

On the Hypermultiplet Moduli Space of Heterotic Compactifications with Small Instantons

We explore a relation between four-dimensional N=2 heterotic vacua induced by Mirror Symmetry via Heterotic/Type II duality. It allows us to compute the α' corrections to the hypermultiplet moduli space of heterotic compactifications on K3xT^2 in the limit of large base of the elliptic K3. We concentrate on the case of point-like instantons on orbifold singularities leading to low-dimensional hypermultiplet moduli spaces.

hep-th↗

arXiv1997

Mirror Symmetry via Deformation of Bundles on K3 Surfaces

We consider F-theory compactifications on a mirror pair of elliptic Calabi-Yau threefolds. This yields two different six-dimensional theories, each of them being nonperturbatively equivalent to some compactification of heterotic strings on a K3 surface S with certain bundle data E --> S. We find evidence for a transformation of S together with the bundle that takes one heterotic model to the other.

hep-th↗

arXiv1997

Matter from Toric Geometry

We present an algorithm for obtaining the matter content of effective six-dimensional theories resulting from compactification of F-theory on elliptic Calabi-Yau threefolds which are hypersurfaces in toric varieties. The algorithm allows us to read off the matter content of the theory from the polyhedron describing the Calabi-Yau manifold. This is based on the generalized Green-Schwarz anomaly cancellation condition.

hep-th↗

arXiv1997

Toric Geometry and Enhanced Gauge Symmetry of F-Theory/Heterotic Vacua

We study F-theory compactified on elliptic Calabi-Yau threefolds that are realised as hypersurfaces in toric varieties. The enhanced gauge group as well as the number of massless tensor multiplets has a very simple description in terms of toric geometry. We find a large number of examples where the gauge group is not a subgroup of E8xE8, but rather, is much bigger (with rank as high as 296). The largest of these groups is the group recently found by Aspinwall and Gross. Our algorithm can also be applied to elliptic fourfolds, for which the groups can become extremely large indeed (with rank as high as 121328). We present the gauge content for two of the fourfolds recently studied by Klemm et al.

hep-th↗

arXiv1997

Enhanced Gauge Symmetry in Type II and F-Theory Compactifications: Dynkin Diagrams from Polyhedra

We explain the observation by Candelas and Font that the Dynkin diagrams of nonabelian gauge groups occurring in type IIA and F-theory can be read off from the polyhedron $Δ^*$ that provides the toric description of the Calabi-Yau manifold used for compacification. We show how the intersection pattern of toric divisors corresponding to the degeneration of elliptic fibers follows the ADE classification of singularities and the Kodaira classification of degenerations. We treat in detail the cases of elliptic K3 surfaces and K3 fibered threefolds where the fiber is again elliptic. We also explain how even the occurrence of monodromy and non-simply laced groups in the latter case is visible in the toric picture. These methods also work in the fourfold case.

hep-th↗

arXiv1997

Comments on A,B,C Chains of Heterotic and Type II Vacua

We construct, as hypersurfaces in toric varieties, Calabi-Yau manifolds corresponding to F-theory vacua dual to E8*E8 heterotic strings compactified to six dimensions on K3 surfaces with non-semisimple gauge backgrounds. These vacua were studied in the recent work of Aldazabal, Font, Ibanez and Uranga. We extend their results by constructing many more examples, corresponding to enhanced gauge symmetries, by noting that they can be obtained from previously known Calabi-Yau manifolds corresponding to K3 compactification of heterotic strings with simple gauge backgrounds by means of extremal transitions of the conifold type.

hep-th↗

arXiv1997

F-Theory Duals of Nonperturbative Heterotic E8xE8 Vacua in Six Dimensions

We present a systematic way of generating F-theory models dual to nonperturbative vacua (i.e., vacua with extra tensor multiplets) of heterotic E8xE8 strings compactified on K3, using hypersurfaces in toric varieties. In all cases, the Calabi-Yau is an elliptic fibration over a blow up of the Hirzebruch surface F_n. We find that in most cases the fan of the base of the elliptic fibration is visible in the dual polyhedron of the Calabi-Yau, and that the extra tensor multiplets are represented as points corresponding to the blow-ups of the F_n.

hep-th↗