Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

Human GC-AG alternative intron isoforms with weak donor sites show enhanced consensus at acceptor exon positions

It has been previously observed that the intrinsically weak variant GC donor sites, in order to be recognized by the U2-type spliceosome, possess strong consensus sequences maximized for base pair formation with U1 and U5/U6 snRNAs. However, variability in signal strength is a fundamental mechanism for splice site selection in alternative splicing. Here we report human alternative GC-AG introns (for the first time from any species), and show that while constitutive GC-AG introns do possess strong signals at their donor sites, a large subset of alternative GC-AG introns possess weak consensus sequences at their donor sites. Surprisingly, this subset of alternative isoforms shows strong consensus at acceptor exon positions 1 and 2. The improved consensus at the acceptor exon can facilitate a strong interaction with U5 snRNA, which tethers the two exons for ligation during the second step of splicing. Further, these isoforms nearly always possess alternative acceptor sites and always possess alternative acceptor sites and exhibit particularly weak polypyrimidine tracts characteristic of AG-dependent introns. The acceptor exon nucleotides are part of the consensus required for the U2AF(35)-mediated recognition of AG in such introns. Such improved consensus at acceptor exons is not found in either normal or alternative GT-AG introns having weak donor sites or weak polypyrimidine,tracts. The changes probably reflect mechanisms that allow GC-AG alternative intron isoforms to cope with two conflicting requirements, namely an apparent need for differential splice strength to direct the choice of alternative sites and a need for improved donor signals to compensate for the central mismatch base pair (C-A) in the RNA duplex of U1 snRNA and the pre-mRNA. The other important findings include (i) one in every twenty alternative introns is a GC-AG intron, and (ii) three of every five observed GC-AG introns are alternative isoforms.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Texture zeros and weak basis transformations

We investigate the physical meaning of some of the "texture zeros" which appear in most of the Ansatze on quark masses and mixings. It is shown that starting from arbitrary quark mass matrices and making a suitable weak basis transformation one can obtain some of these sets of zeros which therefore have no physical content. We then analyse the physical implications of a four-texture zero Ansatz which is in agreement with all present experimental data. (C) 2000 Elsevier Science B.V. AU rights reserved.

Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

From weak Allee effect to no Allee effect in Richards’ growth models

Population dynamics have been attracting interest since many years. Among the considered models, the Richards’ equations remain one of the most popular to describe biological growth processes. On the other hand, Allee effect is currently a major focus of ecological research, which occurs when positive density dependence dominates at low densities. In this chapter, we propose the dynamical study of classes of functions based on Richards’ models describing the existence or not of Allee effect. We investigate bifurcation structures in generalized Richards’ functions and we look for the conditions in the (β, r) parameter plane for the existence of a weak Allee effect region. We show that the existence of this region is related with the existence of a dovetail structure. When the Allee limit varies, the weak Allee effect region disappears when the dovetail structure also disappears. Consequently, we deduce the transition from the weak Allee effect to no Allee effect to this family of functions. To support our analysis, we present fold and flip bifurcation curves and numerical simulations of several bifurcation diagrams.

Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

The identity type weak factorisation system

We show that the classifying category C(T)of a dependent type theory T with axioms for identity types admits a nontrivial weak factorisation system. After characterising this weak factorisation system explicitly, we relate it to the homotopy theory of groupoids.

Do institutions matter for economic fluctuations? Weak property rights in a business cycle model for Mexico

This paper shows that introducing weak property rights in the standard real business cycle (RBC) model can help to explain economic fluctuations. This is motivated by the empirical observation that changes in institutions in emerging markets are related to the evolution of the main macroeconomic variables. In particular, in Mexico, the movements in productivity in the data are associated with changes in institutions, so that we can explain productivity shocks to a large extent as shocks to the quality of institutions. We find that the model with shocks to the degree of protection of property rights only - without technology shocks - can match the second moments in the data for Mexico well. In particular, the fit is better than that of the standard neoclassical model with full protection of property rights regarding the auto-correlations and cross-correlations in the data, especially those related to labor. Viewing productivity shocks as shocks to institutions is also consistent with the stylized fact of falling productivity and non-decreasing labor hours in Mexico over 1980-1994, which is a feature that the neoclassical model cannot match.

Tumor necrosis factor (TNF) signaling, but not TWEAK (TNF-like weak inducer of apoptosis)-triggered cIAP1 (cellular inhibitor of apoptosis protein 1) degradation, requires cIAP1 RING dimerization and E2 binding.

Cellular inhibitor of apoptosis (cIAP) proteins, cIAP1 and cIAP2, are important regulators of tumor necrosis factor (TNF) superfamily (SF) signaling and are amplified in a number of tumor types. They are targeted by IAP antagonist compounds that are undergoing clinical trials. IAP antagonist compounds trigger cIAP autoubiquitylation and degradation. The TNFSF member TWEAK induces lysosomal degradation of TRAF2 and cIAPs, leading to elevated NIK levels and activation of non-canonical NF-kappaB. To investigate the role of the ubiquitin ligase RING domain of cIAP1 in these pathways, we used cIAP-deleted cells reconstituted with cIAP1 point mutants designed to interfere with the ability of the RING to dimerize or to interact with E2 enzymes. We show that RING dimerization and E2 binding are required for IAP antagonists to induce cIAP1 degradation and protect cells from TNF-induced cell death. The RING functions of cIAP1 are required for full TNF-induced activation of NF-kappaB, however, delayed activation of NF-kappaB still occurs in cIAP1 and -2 double knock-out cells. The RING functions of cIAP1 are also required to prevent constitutive activation of non-canonical NF-kappaB by targeting NIK for proteasomal degradation. However, in cIAP double knock-out cells TWEAK was still able to increase NIK levels demonstrating that NIK can be regulated by cIAP-independent pathways. Finally we show that, unlike IAP antagonists, TWEAK was able to induce degradation of cIAP1 RING mutants. These results emphasize the critical importance of the RING of cIAP1 in many signaling scenarios, but also demonstrate that in some pathways RING functions are not required.

Empirical testing of genuine savings as an indicator of weak sustainability: a three-country analysis of long run trends

Genuine Savings has emerged as a widely-used indicator of sustainable development. In this paper, we use long-term data stretching back to 1870 to undertake empirical tests of the relationship between Genuine Savings (GS) and future well-being for three countries: Britain, the USA and Germany. Our tests are based on an underlying theoretical relationship between GS and changes in the present value of future consumption. Based on both single country and panel results, we find evidence supporting the existence of a cointegrating (long run equilibrium) relationship between GS and future well-being, and fail to reject the basic theoretical result on the relationship between these two macroeconomic variables. This provides some support for the GS measure of weak sustainability. We also show the effects of modelling shocks, such as World War Two and the Great Depression.