1,376 research outputs found
Breaking Instance-Independent Symmetries In Exact Graph Coloring
Code optimization and high level synthesis can be posed as constraint
satisfaction and optimization problems, such as graph coloring used in register
allocation. Graph coloring is also used to model more traditional CSPs relevant
to AI, such as planning, time-tabling and scheduling. Provably optimal
solutions may be desirable for commercial and defense applications.
Additionally, for applications such as register allocation and code
optimization, naturally-occurring instances of graph coloring are often small
and can be solved optimally. A recent wave of improvements in algorithms for
Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests
generic problem-reduction methods, rather than problem-specific heuristics,
because (1) heuristics may be upset by new constraints, (2) heuristics tend to
ignore structure, and (3) many relevant problems are provably inapproximable.
Problem reductions often lead to highly symmetric SAT instances, and
symmetries are known to slow down SAT solvers. In this work, we compare several
avenues for symmetry breaking, in particular when certain kinds of symmetry are
present in all generated instances. Our focus on reducing CSPs to SAT allows us
to leverage recent dramatic improvement in SAT solvers and automatically
benefit from future progress. We can use a variety of black-box SAT solvers
without modifying their source code because our symmetry-breaking techniques
are static, i.e., we detect symmetries and add symmetry breaking predicates
(SBPs) during pre-processing.
An important result of our work is that among the types of
instance-independent SBPs we studied and their combinations, the simplest and
least complete constructions are the most effective. Our experiments also
clearly indicate that instance-independent symmetries should mostly be
processed together with instance-specific symmetries rather than at the
specification level, contrary to what has been suggested in the literature
Recurrent proofs of the irrationality of certain trigonometric values
We use recurrences of integrals to give new and elementary proofs of the
irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all
nonzero rational r^2. Immediate consequences to other values of the elementary
transcendental functions are also discussed
Effective slip over superhydrophobic surfaces in thin channels
Superhydrophobic surfaces reduce drag by combining hydrophobicity and
roughness to trap gas bubbles in a micro- and nanoscopic texture. Recent work
has focused on specific cases, such as striped grooves or arrays of pillars,
with limited theoretical guidance. Here, we consider the experimentally
relevant limit of thin channels and obtain rigorous bounds on the effective
slip length for any two-component (e.g. low-slip and high-slip) texture with
given area fractions. Among all anisotropic textures, parallel stripes attain
the largest (or smallest) possible slip in a straight, thin channel for
parallel (or perpendicular) orientation with respect to the mean flow. For
isotropic (e.g. chessboard or random) textures, the Hashin-Strikman conditions
further constrain the effective slip. These results provide a framework for the
rational design of superhydrophobic surfaces.Comment: 4+ page
Synthesis and Optimization of Reversible Circuits - A Survey
Reversible logic circuits have been historically motivated by theoretical
research in low-power electronics as well as practical improvement of
bit-manipulation transforms in cryptography and computer graphics. Recently,
reversible circuits have attracted interest as components of quantum
algorithms, as well as in photonic and nano-computing technologies where some
switching devices offer no signal gain. Research in generating reversible logic
distinguishes between circuit synthesis, post-synthesis optimization, and
technology mapping. In this survey, we review algorithmic paradigms ---
search-based, cycle-based, transformation-based, and BDD-based --- as well as
specific algorithms for reversible synthesis, both exact and heuristic. We
conclude the survey by outlining key open challenges in synthesis of reversible
and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table
Necrotising sinusitis with orbital complication in patient with macrophage activation syndrome (MAS)
Background: Macrophage activation syndrome (MAC) is a potentially fatal clinical-laboratory syndrome of uncontrolled hyperinflammation arising as a result of hereditary or acquired immune-mediated processes of cellular overactivation and nonmalignant proliferation of tissue macrophages/histiocytes, which can cause multiorgan failure.Case report: We present a clinical case of 15-years old child, who was diagnosed with juvenile idiopathic arthritis in 2019. The disease started with macrophage activation syndrome. In the next years the child had multiple hospitalizations in the Pediatrics clinic, but in the course of the disease it developed the picture of severe necrotic pansinuitis with an orbital complication, which required an immediate surgical intervention. Ever since the child had an ongoing necrotizing process in the area of the nasal passages, sinuses, upper jaw and hard palate. Other complications were breakthrough of the hard palate, loss of healthy teeth from the upper dentition and creation of direct communication between the oral cavity and the left maxillary sinus.Conclusions: The diagnosis of MAS is difficult to make, but increased awareness of this disease is an essential for its recognition. The struggle with autoimmune diseases often lasts for years with periods of exacerbation and remission of symptoms. Complications related to them can affect different organs and systems and require interdisciplinary approach
Parity violating cylindrical shell in the framework of QED
We present calculations of Casimir energy (CE) in a system of quantized
electromagnetic (EM) field interacting with an infinite circular cylindrical
shell (which we call `the defect'). Interaction is described in the only
QFT-consistent way by Chern-Simon action concentrated on the defect, with a
single coupling constant .
For regularization of UV divergencies of the theory we use % physically
motivated Pauli-Villars regularization of the free EM action. The divergencies
are extracted as a polynomial in regularization mass , and they renormalize
classical part of the surface action.
We reveal the dependence of CE on the coupling constant . Corresponding
Casimir force is attractive for all values of . For we
reproduce the known results for CE for perfectly conducting cylindrical shell
first obtained by DeRaad and Milton.Comment: Typos corrected. Some references adde
Reversible Logic Circuit Synthesis
Reversible or information-lossless circuits have applications in digital
signal processing, communication, computer graphics and cryptography. They are
also a fundamental requirement in the emerging field of quantum computation. We
investigate the synthesis of reversible circuits that employ a minimum number
of gates and contain no redundant input-output line-pairs (temporary storage
channels). We prove constructively that every even permutation can be
implemented without temporary storage using NOT, CNOT and TOFFOLI gates. We
describe an algorithm for the synthesis of optimal circuits and study the
reversible functions on three wires, reporting distributions of circuit sizes.
We study circuit decompositions of reversible circuits where gates of the same
type are next to each other. Finally, in an application important to quantum
computing, we synthesize oracle circuits for Grover's search algorithm, and
show a significant improvement over a previously proposed synthesis algorithm.Comment: 30 pages, 14 figs+tables. To appear in IEEE Transactions on
Computer-Aided Design of Electronic Circuits. Contains results presented at
the Intl. Conf. on Computer-Aided Design, 2002 and new material on
decompositions of reversible circuits where gates of the same type are next
to each othe
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