On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

Functional sphere profiling reveals the complexity of neuroblastoma tumor-initiating cell model.

Neuroblastoma (NB) is a neural crest-derived childhood tumor characterized by a remarkable phenotypic diversity, ranging from spontaneous regression to fatal metastatic disease. Although the cancer stem cell (CSC) model provides a trail to characterize the cells responsible for tumor onset, the NB tumor-initiating cell (TIC) has not been identified. In this study, the relevance of the CSC model in NB was investigated by taking advantage of typical functional stem cell characteristics. A predictive association was established between self-renewal, as assessed by serial sphere formation, and clinical aggressiveness in primary tumors. Moreover, cell subsets gradually selected during serial sphere culture harbored increased in vivo tumorigenicity, only highlighted in an orthotopic microenvironment. A microarray time course analysis of serial spheres passages from metastatic cells allowed us to specifically "profile" the NB stem cell-like phenotype and to identify CD133, ABC transporter, and WNT and NOTCH genes as spheres markers. On the basis of combined sphere markers expression, at least two distinct tumorigenic cell subpopulations were identified, also shown to preexist in primary NB. However, sphere markers-mediated cell sorting of parental tumor failed to recapitulate the TIC phenotype in the orthotopic model, highlighting the complexity of the CSC model. Our data support the NB stem-like cells as a dynamic and heterogeneous cell population strongly dependent on microenvironmental signals and add novel candidate genes as potential therapeutic targets in the control of high-risk NB.

Complexity and Bounded Rationality in Individual Decision Problemsing.

I develop a model of endogenous bounded rationality due to search costs, arising implicitly from the problems complexity. The decision maker is not required to know the entire structure of the problem when making choices but can think ahead, through costly search, to reveal more of it. However, the costs of search are not assumed exogenously; they are inferred from revealed preferences through her choices. Thus, bounded rationality and its extent emerge endogenously: as problems become simpler or as the benefits of deeper search become larger relative to its costs, the choices more closely resemble those of a rational agent. For a fixed decision problem, the costs of search will vary across agents. For a given decision maker, they will vary across problems. The model explains, therefore, why the disparity, between observed choices and those prescribed under rationality, varies across agents and problems. It also suggests, under reasonable assumptions, an identifying prediction: a relation between the benefits of deeper search and the depth of the search. As long as calibration of the search costs is possible, this can be tested on any agent-problem pair. My approach provides a common framework for depicting the underlying limitations that force departures from rationality in different and unrelated decision-making situations. Specifically, I show that it is consistent with violations of timing independence in temporal framing problems, dynamic inconsistency and diversification bias in sequential versus simultaneous choice problems, and with plausible but contrasting risk attitudes across small- and large-stakes gambles.

Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0.

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

Measuring Tax Complexity

This paper critically examines a number of issues relating to the measurement of tax complexity. It starts with an analysis of the concept of tax complexity, distinguishing tax design complexity and operational complexity. It considers the consequences/costs of complexity, and then examines the rationale for measuring complexity. Finally it applies the analysis to an examination of an index of complexity developed by the UK Office of Tax Simplification (OTS).

Identification of case complexity and increased health care utilization in patients with rheumatoid arthritis.

OBJECTIVES: To document biopsychosocial profiles of patients with rheumatoid arthritis (RA) by means of the INTERMED and to correlate the results with conventional methods of disease assessment and health care utilization. METHODS: Patients with RA (n = 75) were evaluated with the INTERMED, an instrument for assessing case complexity and care needs. Based on their INTERMED scores, patients were compared with regard to severity of illness, functional status, and health care utilization. RESULTS: In cluster analysis, a 2-cluster solution emerged, with about half of the patients characterized as complex. Complex patients scoring especially high in the psychosocial domain of the INTERMED were disabled significantly more often and took more psychotropic drugs. Although the 2 patient groups did not differ in severity of illness and functional status, complex patients rated their illness as more severe on subjective measures and on most items of the Medical Outcomes Study Short Form 36. Complex patients showed increased health care utilization despite a similar biologic profile. CONCLUSIONS: The INTERMED identified complex patients with increased health care utilization, provided meaningful and comprehensive patient information, and proved to be easy to implement and advantageous compared with conventional methods of disease assessment. Intervention studies will have to demonstrate whether management strategies based on INTERMED profiles can improve treatment response and outcome of complex patients.

Transitions in social complexity along elevational gradients reveal a combined impact of season length and development time on social evolution.

Eusociality is taxonomically rare, yet associated with great ecological success. Surprisingly, studies of environmental conditions favouring eusociality are often contradictory. Harsh conditions associated with increasing altitude and latitude seem to favour increased sociality in bumblebees and ants, but the reverse pattern is found in halictid bees and polistine wasps. Here, we compare the life histories and distributions of populations of 176 species of Hymenoptera from the Swiss Alps. We show that differences in altitudinal distributions and development times among social forms can explain these contrasting patterns: highly social taxa develop more quickly than intermediate social taxa, and are thus able to complete the reproductive cycle in shorter seasons at higher elevations. This dual impact of altitude and development time on sociality illustrates that ecological constraints can elicit dynamic shifts in behaviour, and helps explain the complex distribution of sociality across ecological gradients.

GWAS of human bitter taste perception identifies new loci and reveals additional complexity of bitter taste genetics.

Human perception of bitterness displays pronounced interindividual variation. This phenotypic variation is mirrored by equally pronounced genetic variation in the family of bitter taste receptor genes. To better understand the effects of common genetic variations on human bitter taste perception, we conducted a genome-wide association study on a discovery panel of 504 subjects and a validation panel of 104 subjects from the general population of São Paulo in Brazil. Correction for general taste-sensitivity allowed us to identify a SNP in the cluster of bitter taste receptors on chr12 (10.88- 11.24 Mb, build 36.1) significantly associated (best SNP: rs2708377, P = 5.31 × 10(-13), r(2) = 8.9%, β = -0.12, s.e. = 0.016) with the perceived bitterness of caffeine. This association overlaps with-but is statistically distinct from-the previously identified SNP rs10772420 influencing the perception of quinine bitterness that falls in the same bitter taste cluster. We replicated this association to quinine perception (P = 4.97 × 10(-37), r(2) = 23.2%, β = 0.25, s.e. = 0.020) and additionally found the effect of this genetic locus to be concentration specific with a strong impact on the perception of low, but no impact on the perception of high concentrations of quinine. Our study, thus, furthers our understanding of the complex genetic architecture of bitter taste perception.

Analyzing complexity in foreign language monologic oral production in a CLIL context

The study tested three analytic tools applied in SLA research (T-unit, AS-unit and Idea-unit) against FL learner monologic oral data. The objective was to analyse their effectiveness for the assessment of complexity of learners' academic production in English. The data were learners' individual productions gathered during the implementation of a CLIL teaching sequence on Natural Sciences in a Catalan state secondary school. The analysis showed that only AS-unit was easily applicable and highly effective in segmenting the data and taking complexity measures

What do we gain from simplicity versus complexity in species distribution models?

Species distribution models (SDMs) are widely used to explain and predict species ranges and environmental niches. They are most commonly constructed by inferring species' occurrence-environment relationships using statistical and machine-learning methods. The variety of methods that can be used to construct SDMs (e.g. generalized linear/additive models, tree-based models, maximum entropy, etc.), and the variety of ways that such models can be implemented, permits substantial flexibility in SDM complexity. Building models with an appropriate amount of complexity for the study objectives is critical for robust inference. We characterize complexity as the shape of the inferred occurrence-environment relationships and the number of parameters used to describe them, and search for insights into whether additional complexity is informative or superfluous. By building 'under fit' models, having insufficient flexibility to describe observed occurrence-environment relationships, we risk misunderstanding the factors shaping species distributions. By building 'over fit' models, with excessive flexibility, we risk inadvertently ascribing pattern to noise or building opaque models. However, model selection can be challenging, especially when comparing models constructed under different modeling approaches. Here we argue for a more pragmatic approach: researchers should constrain the complexity of their models based on study objective, attributes of the data, and an understanding of how these interact with the underlying biological processes. We discuss guidelines for balancing under fitting with over fitting and consequently how complexity affects decisions made during model building. Although some generalities are possible, our discussion reflects differences in opinions that favor simpler versus more complex models. We conclude that combining insights from both simple and complex SDM building approaches best advances our knowledge of current and future species ranges.

Strong isomorphism reductions in complexity theory

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees.