Tag schemes [23 articles]

Abstract

A quasi-coherent ringed scheme is a pair (X,A), where X is a scheme, and A is a noncommutative quasi-coherent O_X-ring. We introduce dualizing complexes over quasi-coherent ringed schemes and study their properties. For a separated differential quasi-coherent ringed scheme of finite type over a field, we prove existence and uniqueness of a rigid dualizing complex. In the proof we use the theory of perverse coherent sheaves in order to glue local pieces of the rigid dualizing complex into a global complex. ...

Abstract

The theory of schemes is the foundation for algebraic geometry proposed andelaborated by Alexander Grothendieck and his co-workers. It has allowed majorprogress in classical areas of algebraic geometry such as invariant theory andthe moduli of curves. It integrates algebraic number theory with algebraicgeometry, fulfilling the dreams of earlier generations of number theorists.This integration has led to proofs of some of the major conjectures in numbertheory (Deligne's proof of the Weil Conjectures, Faltings' proof of theMordell Conjecture).This book is intended to bridge ...

Abstract

The second volume of Shafarevich's introductory book on algebraic varietiesand complex manifolds. As with Volume 1, the author has revised the text andadded new material, e.g. as a section on real algebraic curves. Although thematerial is more advanced than in Volume 1 the algebraic apparatus is kept toa minimum, making the book accessible to non-specialists. It can be readindependently of Volume 1 and is suitable for beginning graduate students inmathematics as well as those in theoretical physics. ...

Abstract

This volume of the _Encyclopaedia_ consists of two parts. The first is devotedto the theory of curves, which are treated from both the analytic andalgebraic points of view. Starting with the basic notions of the theory ofRiemann surfaces the reader is lead into an exposition covering the Riemann-Roch theorem, Riemann's fundamental existence theorem, uniformization andautomorphic functions. The algebraic material also treats algebraic curvesover an arbitrary field and the connection between algebraic curves andAbelian varieties. The second part is an introduction to ...

Abstract

We present a framework for designing end-to-end congestion control schemes in a network where each user may have a different utility function and may experience noncongestion-related losses. We first show that there exists an additive-increase-multiplicative-decrease scheme using only end-to-end measurable losses such that a socially optimal solution can be reached. We incorporate round-trip delay in this model, and show that one can generalize observations regarding TCP-type congestion avoidance to more general window flow control schemes. We then consider explicit congestion notification ...

Abstract

For nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are implicit in the diffusion vector fields. They thus apply to a restricted class, namely those with sublinear form. This however, still includes most Langevin derived processes typical of volatility models in finance and molecular simulation in physics. When the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process. We thus consider the non-central chi-squared transition ...

Abstract

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we assign the complex Hom^cont_X(C(X),M) of continuous Hochschild cochains with values in M. Our first main result is that when X is smooth over K there is a functorial isomorphism between the complex of continuous Hochschild cochains and RHom_X2(O_X,M), in the derived category D(Mod(O_X2)). The second main result ...

Abstract

This preprint appeared firstly in Russian in 1997. Some truncated versions of this preprint were published in English and French, here a fully translated version is presented. The translation in English was done by O. V. Feodoritova and V. Deledicque to whom I express my gratitude. In the present paper I will describe how the first variant of the Godunov's scheme has been elaborated in 1953-1954 and tell about all modifications realized by myself (until 1969) and the group of scientists from the Institute of Applied Mathematics in ...

Abstract

Encryption is one of the fundamental technologies that is used in digital rights management. Unlike ordinary computer applications, multimedia applications generate large amounts of data that has to be processed in real time. So, a number of encryption schemes for multimedia applications have been proposed in recent years. We analyze the following proposed methods for multimedia encryption: key-based multiple Huffman tables (MHT), arithmetic coding with key-based interval splitting (KSAC), and randomized arithmetic coding (RAC). Our analysis shows that MHT and KSAC ...

Abstract

An undesirable side effect of many watermarking and data-hiding schemes is that the host signal into which auxiliary data is embedded is distorted. Finding an optimal balance between the amount of information embedded and the induced distortion is therefore an active field of research. With the rediscovery of Costa's (1983) seminal paper entitled Writing on dirty paper, there has been considerable progress in understanding the fundamental limits of the capacity versus distortion of watermarking and data-hiding schemes. For some applications, however, ...

Abstract

After conquering the core and metropolitan networks, fiber is now penetrating into the access domain. Its low loss and huge bandwidth enable the delivery of any current and foreseeable set of broadband services, and also make it a nice match to the wireless link to the end user. Cost effectiveness is a key issue, and will be decisive for the network topology choices. Point-to-point may be the most cost-effective for short-reach access, whereas point-to-multipoint may be the most interesting at medium- ...

Abstract

Due to the open, anonymous nature of many P2P networks, new identities - or sybils - may be created cheaply and in large numbers. Given a reputation system, a peer may attempt to falsely raise its reputation by creating fake links between its sybils. Many existing reputation mechanisms are not resistant to these types of strategies.Using a static graph formulation of reputation, we attempt to formalize the notion of sybilproofness. We show that there is no symmetric sybilproof reputation function. For ...

Abstract

We present a content-driven reputation system for Wikipedia authors. In our system, authors gain reputation when the edits they perform to Wikipedia articles are preserved by subsequent authors, and they lose reputation when their edits are rolled back or undone in short order. Thus, author reputation is computed solely on the basis of content evolution; user-to-user comments or ratings are not used. The author reputation we compute could be used to flag new contributions from low-reputation authors, or it ...

Abstract

An unusual pattern in a nucleic acid or protein sequence or a region of strong similarity shared by two or more sequences may have biological significance. It is therefore desirable to know whether such a pattern can have arisen simply by chance. To identify interesting sequence patterns, appropriate scoring values can be assigned to the individual residues of a single sequence or to sets of residues when several sequences are compared. For single sequences, such scores can reflect biophysical properties such ...

Abstract

We present a novel peer-to-peer backup technique that allows computers connected to the Internet to back up their data cooperatively: Each computer has a set of partner computers, which collectively hold its backup data. In return, it holds a part of each partner's backup data. By adding redundancy and distributing the backup data across many partners, a highly-reliable backup can be obtained in spite of the low reliability of the average Internet machine. <P> Because our scheme requires cooperation, it is ...

Abstract

We explain how to award a monopoly franchise so as to maximize expected consumers' welfare. Potential producers initially possess imperfect private information about production cost. The franchise is awarded to the producer with the lowest expected costs, but prices exceed realized marginal costs. These ex post distortions foster more competitive bidding ex ante. The distortions for any bid-cost pair are invariant to the number of bidders (n), though expected distortions and profits decline with n. ...

Abstract

This article considers a two-period model of natural monopoly and second-sourcing. The incumbent supplier invests in the first period. After observing the incumbent's first-period performance, the buyer may break out in the second period. The investment may or may not be transferable to the second source, and it may be monetary or take the form of human capital. We determine whether the incumbent should be favored at the reprocurement stage, and how the slope of his incentive scheme should evolve over ...