Irreducible morphisms of categories of complexes

We study irreducible morphisms of complexes. In particular, we show that the irreducible morphisms having one (finite) irreducible submorphism fall into three canonical forms and we give necessary and sufficient conditions for a given morphism of that type to be irreducible. Our characterization of the above mentioned type of irreducible morphisms of complexes characterizes also some class of irreducible morphisms of the derived category D(-)(A) for A a finite dimensional k-algebra, where k is a field. (C) 2009 Published by Elsevier Inc.

A NOTE ON THE COMPOSITE OF TWO IRREDUCIBLE MORPHISMS

In this note, we show that a composite of two irreducible morphisms between indecomposable modules cannot lie in R(3)\R(5).

On the composite of irreducible morphisms in almost sectional paths

We study here when the composite of it irreducible morphisms in almost sectional paths is non-zero and lies in Rn+1 (C) 2007 Elsevier B.V. All rights reserved.

ON THE COMPOSITE OF THREE IRREDUCIBLE MORPHISMS IN THE FOURTH POWER OF THE RADICAL

We study here the nonzero composite of three irreducible morphisms between indecomposable modules lying in the fourth power of the radical.

Optimistic linear programming gives logarithmic regret for irreducible MDPs

We present an algorithm called Optimistic Linear Programming (OLP) for learning to optimize average reward in an irreducible but otherwise unknown Markov decision process (MDP). OLP uses its experience so far to estimate the MDP. It chooses actions by optimistically maximizing estimated future rewards over a set of next-state transition probabilities that are close to the estimates, a computation that corresponds to solving linear programs. We show that the total expected reward obtained by OLP up to time T is within C(P) log T of the reward obtained by the optimal policy, where C(P) is an explicit, MDP-dependent constant. OLP is closely related to an algorithm proposed by Burnetas and Katehakis with four key differences: OLP is simpler, it does not require knowledge of the supports of transition probabilities, the proof of the regret bound is simpler, but our regret bound is a constant factor larger than the regret of their algorithm. OLP is also similar in flavor to an algorithm recently proposed by Auer and Ortner. But OLP is simpler and its regret bound has a better dependence on the size of the MDP.

The Parity of the Number of Irreducible Factors for Some Pentanomials

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials.

Parity of the Number of Irreducible Factors for Composite Polynomials

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.

Divisibility of Trinomials by Irreducible Polynomials over F_2

Irreducible trinomials of given degree n over F_2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F_2. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over F_2 is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials x^m + x^s + 1 to the trinomials x^am + x^bs + 1.

Irreducible uncertainty in near-term climate projections

Model simulations of the next few decades are widely used in assessments of climate change impacts and as guidance for adaptation. Their non-linear nature reveals a level of irreducible uncertainty which it is important to understand and quantify, especially for projections of near-term regional climate. Here we use large idealised initial condition ensembles of the FAMOUS global climate model with a 1 %/year compound increase in CO2 levels to quantify the range of future temperatures in model-based projections. These simulations explore the role of both atmospheric and oceanic initial conditions and are the largest such ensembles to date. Short-term simulated trends in global temperature are diverse, and cooling periods are more likely to be followed by larger warming rates. The spatial pattern of near-term temperature change varies considerably, but the proportion of the surface showing a warming is more consistent. In addition, ensemble spread in inter-annual temperature declines as the climate warms, especially in the North Atlantic. Over Europe, atmospheric initial condition uncertainty can, for certain ocean initial conditions, lead to 20 year trends in winter and summer in which every location can exhibit either strong cooling or rapid warming. However, the details of the distribution are highly sensitive to the ocean initial condition chosen and particularly the state of the Atlantic meridional overturning circulation. On longer timescales, the warming signal becomes more clear and consistent amongst different initial condition ensembles. An ensemble using a range of different oceanic initial conditions produces a larger spread in temperature trends than ensembles using a single ocean initial condition for all lead times. This highlights the potential benefits from initialising climate predictions from ocean states informed by observations. These results suggest that climate projections need to be performed with many more ensemble members than at present, using a range of ocean initial conditions, if the uncertainty in near-term regional climate is to be adequately quantified.

Atmospheric and oceanic contributions to irreducible forecast uncertainty of Arctic surface climate

Uncertainty of Arctic seasonal to interannual predictions arising from model errors and initial state uncertainty has been widely discussed in the literature, whereas the irreducible forecast uncertainty (IFU) arising from the chaoticity of the climate system has received less attention. However, IFU provides important insights into the mechanisms through which predictability is lost, and hence can inform prioritization of model development and observations deployment. Here, we characterize how internal oceanic and surface atmospheric heat fluxes contribute to IFU of Arctic sea ice and upper ocean heat content in an Earth system model by analyzing a set of idealized ensemble prediction experiments. We find that atmospheric and oceanic heat flux are often equally important for driving unpredictable Arctic-wide changes in sea ice and surface water temperatures, and hence contribute equally to IFU. Atmospheric surface heat flux tends to dominate Arctic-wide changes for lead times of up to a year, whereas oceanic heat flux tends to dominate regionally and on interannual time scales. There is in general a strong negative covariance between surface heat flux and ocean vertical heat flux at depth, and anomalies of lateral ocean heat transport are wind-driven, which suggests that the unpredictable oceanic heat flux variability is mainly forced by the atmosphere. These results are qualitatively robust across different initial states, but substantial variations in the amplitude of IFU exist. We conclude that both atmospheric variability and the initial state of the upper ocean are key ingredients for predictions of Arctic surface climate on seasonal to interannual time scales.

Blind equalization of non-irreducible and non-column-reduced channels driven by constant modulus signals

We address the blind equalization of finite-impulse-response (FIR), multiple-input multiple-output (MIMO) channels excited by constant modulus (CM) signals. It is known that the algorithms based on the constant modulus (CM) criterion can equalize an FIR MIMO channel that is irreducible and column-reduced. We show in this paper that the CM property of signals can be exploited to construct a zero-forcing equalizer for a non-irreducible and non-column-reduced channel. We also give a lower bound for the order of the equalizer. Simulation examples demonstrate the proposed result.

Blind equalization of non-irreducible channels driven by MPSK signals

This paper deals with the problem of blind equalization of finite-impulse-response (FIR) and multiple-input multiple-output (MIMO) channels excited by M-ary phase shift keying (MPSK) signals. It is known that the algorithms based on the constant modulus (CM) criterion can equalize an FIR MIMO channel that is irreducible. The irreducible condition is restrictive since it requires that all source signals arrive at the receiving antennas simultaneously. In this paper, we show that the CM criterion can also be used to construct a zero-forcing equalizer for a channel that is non-irreducible. We also derive a lower bound for the order of the equalizer. The proposed result is validated by numerical simulations.