4,535 research outputs found
K-theory and 0-cycles on schemes
We prove Bloch's formula for 0-cycles on affine schemes over algebraically
closed fields. We prove this formula also for projective schemes over
algebraically closed fields which are regular in codimension one. Several
applications, including Bloch's formula for 0-cycles with modulus, are derived.Comment: 40 pages, Final version, to appear in J. Algebraic Geom. (JAG
Zero-cycles with modulus and relative -theory
We construct a cycle class map from the higher Chow groups of 0-cycles to the
relative -theory of a modulus pair. We show that this induces a
pro-isomorphism between the additive higher Chow groups of relative 0-cycles
and relative -theory of truncated polynomial rings over a regular semi-local
ring, essentially of finite type over a characteristic zero field.Comment: Minor revision, Final version, 47 pages, to appear in Annals of
K-Theor
FPGA based hybrid architecture for parallelizing RRT
Field Programmable Gate Arrays(FPGA) exceed the computing power of software
based implementations by breaking the paradigm of sequential execution and
accomplishing more per clock cycle by enabling hardware level parallelization
at an architectural level. Introducing parallel architectures for a
computationally intensive algorithm like Rapidly Exploring Random Trees(RRT)
will result in an exploration that is fast, dense and uniform. Through a cost
function delineated in later sections, FPGA based combinatorial architecture
delivers superlative speed-up but consumes very high power while hierarchical
architecture delivers relatively lower speed-up with acceptable power
consumption levels. To combine the qualities of both, a hybrid architecture,
that encompasses both combinatorial and hierarchical architecture, is designed.
To determine the number of RRT nodes to be allotted to the combinatorial and
hierarchical blocks of the hybrid architecture, a cost function, comprised of
fundamentally inversely related speed-up and power parameters, is formulated.
This maximization of cost function, with its associated constraints,is then
mathematically solved using a modified branch and bound, that leads to optimal
allocation of RRT modules to both blocks. It is observed that this hybrid
architecture delivers the highest performance-per-watt out of the three
architectures for differential, quad-copter and fixed wing kinematics
IMSuite: A Benchmark Suite for Simulating Distributed Algorithms
Considering the diverse nature of real-world distributed applications that
makes it hard to identify a representative subset of distributed benchmarks, we
focus on their underlying distributed algorithms. We present and characterize a
new kernel benchmark suite (named IMSuite) that simulates some of the classical
distributed algorithms in task parallel languages. We present multiple
variations of our kernels, broadly categorized under two heads: (a) varying
synchronization primitives (with and without fine grain synchronization
primitives); and (b) varying forms of parallelization (data parallel and
recursive task parallel). Our characterization covers interesting aspects of
distributed applications such as distribution of remote communication requests,
number of synchronization, task creation, task termination and atomic
operations. We study the behavior (execution time) of our kernels by varying
the problem size, the number of compute threads, and the input configurations.
We also present an involved set of input generators and output validators
Lexical State Analyzer
Lexical states provide a powerful mechanism to scan regular expressions in a
context sensitive manner. At the same time, lexical states also make it hard to
reason about the correctness of the grammar. We first categorize the related
correctness issues into two classes: errors and warnings, and then present a
context sensitive and a context insensitive analysis to identify errors and
warnings in context-free-grammars (CFGs). We also present a comparative study
of these analyses. A standalone tool (LSA) has also been implemented by us that
can identify errors and warnings in JavaCC grammars. The LSA tool outputs a
graph that depicts the grammar and the error transitions. It can also generates
counter example strings that can be used to establish the errors. We have used
LSA to analyze a host of open-source JavaCC grammar files to good effect.Comment: 16 pages, 11 figure
Momentum Dependent Higher Partial Wave Interactions in Bose Einstein condensate
We have investigated the role of momentum dependent s-wave and higher partial
wave strong interactions to determine the ground state properties and the
column densities in the Bose-Einstein condensate (BEC) for large scattering
length (a) such that ka >>1 even for small values of momentum where the
momentum p=(h/2pi)k and k is the wave number. Since the scattering length is
large we have included the first correction (Lee-Huang-Yang correction) both
for the k-dependent (s-wave + higher partial wave) interactions and
k-independent contact interactions (s-wave). We have derived the
time-independent equations from the corresponding energy functionals and found
that the ground state properties and the column densities differ significantly
for these two types of interactions even for moderate values of scattering
length (a = 3000 a_0) in BEC of cylindrically trapped 85Rb atoms at 100 nK. The
effect of higher partial wave (d-wave) increases with increase in a and it is >
20% for peak density at a= 8700 a_0 which can be experimentally detected.
Dependence of column density on particle number density has been studied.
Column densities have been compared with experimental results.Comment: 9 pages, 2 figure
Bounds on Fractional Repetition Codes using Hypergraphs
In the \textit{Distributed Storage Systems} (DSSs), an encoded fraction of
information is stored in the distributed fashion on different chunk servers.
Recently a new paradigm of \textit{Fractional Repetition} (FR) codes have been
introduced, in which, encoded data information is stored on distributed
servers, where encoding is done using a \textit{Maximum Distance Separable}
(MDS) code and a smart replication of packets. In this work, we have shown that
an FR code is equivalent to a hypergraph. Using the correspondence, the
properties and the bounds of a hypergraph are directly mapped to the associated
FR code. In general, the necessary and sufficient conditions for the existence
of an FR code is obtained by using the correspondence. Some of the bounds are
new and FR codes meeting these bounds are unknown. It is also shown that any FR
code associated with a linear hypergraph is universally good.Comment: 8 pages, 2 figure
On Heterogeneous Regenerating Codes and Capacity of Distributed Storage Systems
Heterogeneous Distributed Storage Systems (DSS) are close to real world
applications for data storage. Internet caching system and peer-to-peer storage
clouds are the examples of such DSS. In this work, we calculate the capacity
formula for such systems where each node store different number of packets and
each having a different repair bandwidth (node can be repaired by contacting a
specific set of nodes). The tradeoff curve between storage and repair bandwidth
is studied for such heterogeneous DSS. By analyzing the capacity formula new
minimum bandwidth regenerating (MBR) and minimum storage regenerating (MBR)
points are obtained on the curve. It is shown that in some cases these are
better than the homogeneous DSS.Comment: submitted to conference Netcod 2014, 3 figures, 5 page
Tradeoff for Heterogeneous Distributed Storage Systems between Storage and Repair Cost
In this paper, we consider heterogeneous distributed storage systems (DSSs)
having flexible reconstruction degree, where each node in the system has
dynamic repair bandwidth and dynamic storage capacity. In particular, a data
collector can reconstruct the file at time using some arbitrary nodes in
the system and for a node failure the system can be repaired by some set of
arbitrary nodes. Using - bound, we investigate the fundamental
tradeoff between storage and repair cost for our model of heterogeneous DSS. In
particular, the problem is formulated as bi-objective optimization linear
programing problem. For an arbitrary DSS, it is shown that the calculated
- bound is tight.Comment: 10 pages, 5 figures, draf
On Code Rates of Fractional Repetition Codes
In \textit{Distributed Storage Systems} (DSSs), usually, data is stored using
replicated packets on different chunk servers. Recently a new paradigm of
\textit{Fractional Repetition} (FR) codes have been introduced, in which, data
is replicated in a smart way on distributed servers using a \textit{Maximum
Distance Separable} (MDS) code. In this work, for a non-uniform FR code, bounds
on the FR code rate and DSS code rate are studied. Using matrix representation
of an FR code, some universally good FR codes have been obtained.Comment: 11 pages, 0 figure
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