16,909 research outputs found
A 14-dimensional module for the symplectic group: orbits on vectors
Let F be a field, V a 6-dimensional F-vector space and f a nondegenerate alternating bilinear form on V. We consider a 14-dimensional module for the symplectic group Sp(V, f) congruent to Sp(6, F) associated with (V, f), and classify the orbits on vectors. For characteristic distinct from 2, this module is irreducible and isomorphic to the Weyl module of Sp(V, f) for the fundamental weight lambda(3). If the characteristic is 2, then the module is reducible as it contains an 8-dimensional submodule isomorphic to the spin module of Sp(V, f)
Optimal Sparsification for Some Binary CSPs Using Low-degree Polynomials
This paper analyzes to what extent it is possible to efficiently reduce the
number of clauses in NP-hard satisfiability problems, without changing the
answer. Upper and lower bounds are established using the concept of
kernelization. Existing results show that if NP is not contained in coNP/poly,
no efficient preprocessing algorithm can reduce n-variable instances of CNF-SAT
with d literals per clause, to equivalent instances with bits for
any e > 0. For the Not-All-Equal SAT problem, a compression to size
exists. We put these results in a common framework by analyzing
the compressibility of binary CSPs. We characterize constraint types based on
the minimum degree of multivariate polynomials whose roots correspond to the
satisfying assignments, obtaining (nearly) matching upper and lower bounds in
several settings. Our lower bounds show that not just the number of
constraints, but also the encoding size of individual constraints plays an
important role. For example, for Exact Satisfiability with unbounded clause
length it is possible to efficiently reduce the number of constraints to n+1,
yet no polynomial-time algorithm can reduce to an equivalent instance with
bits for any e > 0, unless NP is a subset of coNP/poly.Comment: Updated the cross-composition in lemma 18 (minor update), since the
previous version did NOT satisfy requirement 4 of lemma 18 (the proof of
Claim 20 was incorrect
FPT is Characterized by Useful Obstruction Sets
Many graph problems were first shown to be fixed-parameter tractable using
the results of Robertson and Seymour on graph minors. We show that the
combination of finite, computable, obstruction sets and efficient order tests
is not just one way of obtaining strongly uniform FPT algorithms, but that all
of FPT may be captured in this way. Our new characterization of FPT has a
strong connection to the theory of kernelization, as we prove that problems
with polynomial kernels can be characterized by obstruction sets whose elements
have polynomial size. Consequently we investigate the interplay between the
sizes of problem kernels and the sizes of the elements of such obstruction
sets, obtaining several examples of how results in one area yield new insights
in the other. We show how exponential-size minor-minimal obstructions for
pathwidth k form the crucial ingredient in a novel OR-cross-composition for
k-Pathwidth, complementing the trivial AND-composition that is known for this
problem. In the other direction, we show that OR-cross-compositions into a
parameterized problem can be used to rule out the existence of efficiently
generated quasi-orders on its instances that characterize the NO-instances by
polynomial-size obstructions.Comment: Extended abstract with appendix, as accepted to WG 201
On volatile element trends in gas-rich meteorites
Ten volatile elements (and non-volatile Co) in co-existing light and dark portions of 5 gas-rich chondrites were studied. Patterns of distinct but non-uniform enrichment by dark admixing material are revealed. The dark admixing material is enriched in Cs; Bi and Tl covary in it. It is compositionally unique from known types of primitive materials and is apparently not derived by secondary processes from such materials
Deformation rings which are not local complete intersections
We study the inverse problem for the versal deformation rings
of finite dimensional representations of a finite group over a
field of positive characteristic . This problem is to determine which
complete local commutative Noetherian rings with residue field can arise up
to isomorphism as such . We show that for all integers
and all complete local commutative Noetherian rings with residue
field , the ring arises in this way. This
ring is not a local complete intersection if , so we
obtain an answer to a question of M. Flach in all characteristics.Comment: 16 page
A Litner Model of Payout and Managerial Rents
We develop a dynamic agency model where payout, investment and financing decisions are made by managers who attempt to maximize the rents they take from the firm, subject to a capital market constraint. Managers smooth payout in order to smooth their flow of rents. Total payout (dividends plus net repurchases) follows Lintner's (1956) target-adjustment model. Payout smooths out transitory shocks to current income and adjusts gradually to changes in permanent income. Smoothing is accomplished by borrowing or lending. Payout is not cut back to finance capital investment. Risk aversion causes managers to underinvest, but habit formation mitigates the degree of underinvestment.
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