140 research outputs found
Markov bases and subbases for bounded contingency tables
In this paper we study the computation of Markov bases for contingency tables
whose cell entries have an upper bound. In general a Markov basis for unbounded
contingency table under a certain model differs from a Markov basis for bounded
tables. Rapallo, (2007) applied Lawrence lifting to compute a Markov basis for
contingency tables whose cell entries are bounded. However, in the process, one
has to compute the universal Gr\"obner basis of the ideal associated with the
design matrix for a model which is, in general, larger than any reduced
Gr\"obner basis. Thus, this is also infeasible in small- and medium-sized
problems. In this paper we focus on bounded two-way contingency tables under
independence model and show that if these bounds on cells are positive, i.e.,
they are not structural zeros, the set of basic moves of all
minors connects all tables with given margins. We end this paper with an open
problem that if we know the given margins are positive, we want to find the
necessary and sufficient condition on the set of structural zeros so that the
set of basic moves of all minors connects all incomplete
contingency tables with given margins.Comment: 22 pages. It will appear in the Annals of the Institution of
Statistical Mathematic
Assessment of the economic and social impact using SROI: An application to sport companies
This paper evaluates the social impact of a football club and its philanthropic organization on the local community and its stakeholders, namely supporters, sponsors, players, and shopkeepers. The methodology used is the Social Return on Investment (SROI). SROI methodology includes all the beneficiaries that are beyond the scope of the company's accounting and its fiscal and financial statements. The aim is to assess both the benefits and the negative impacts of a company's activities on stakeholders. This type of analysis combines the use of qualitative, quantitative and financial information gathered and analyzes them in order to estimate the amount of "value", including mental health and well-being, created or destroyed by a business activity, by a project or by the overall operation of an organization. The sport club under review in the present analysis is called Virtus Entella, an Italian football club playing in the second division. An SROI indicator was applied in reference to the business activity that took place during the championship season 2017/2018. Results show that the social impact created during the championship amounts to approximately 44 million Euro against a financial investment of 15 million Euro, producing an SROI ratio of 2.98:1. This outcome suggests that for every euro invested by the football club, about 3 Euros of social value is created
Semi-Markov Graph Dynamics
In this paper, we outline a model of graph (or network) dynamics based on two
ingredients. The first ingredient is a Markov chain on the space of possible
graphs. The second ingredient is a semi-Markov counting process of renewal
type. The model consists in subordinating the Markov chain to the semi-Markov
counting process. In simple words, this means that the chain transitions occur
at random time instants called epochs. The model is quite rich and its possible
connections with algebraic geometry are briefly discussed. Moreover, for the
sake of simplicity, we focus on the space of undirected graphs with a fixed
number of nodes. However, in an example, we present an interbank market model
where it is meaningful to use directed graphs or even weighted graphs.Comment: 25 pages, 4 figures, submitted to PLoS-ON
Incidence of prosthesis-patient mismatch in patients receiving mitral Biocor® porcine prosthetic valves
Background: The aim was to assess the incidence of prosthesis-patient mismatch (PPM) after mitral valve replacement (MVR) in patients receiving Biocor® porcine or mechanical valves, and to evaluate the effect of PPM on long-term survival.
Methods: All patients undergoing MVR between 2009 and 2013 received either mechanical or bioprosthetic valves (Biocor® porcine). PPM was defined as severe when the indexed effective oriÂfice area was < 0.9 cm2/m2, moderate between 0.9 cm2/m2 and 1.2 cm2/m2 or absent > 1.2 cm2/m2. The primary endpoint was all-cause long-term mortality.
Results: Among a total of 136 MVR, PPM was severe in 27%, moderate in 44% and absent in 29% of patients. Implanted valves were 57% mechanical and 43% bioprosthetic. Only 3% of patients with mechanical valves had severe PPM vs. 59% with bioprostheses (p < 0.0001). Sixty-month survival with severe mismatch was 0.559 (SE 0.149) and with no mismatch 0.895 (SE 0.058) (p = 0.043). Survival of patients suffering from severe mismatch, or moderate mismatch with pulmonary hypertension (PH) was 0.749 (SE 0.101); while for patients with no mismatch or with moderate mismatch without PH, survival was 0.951 (SE 0.028) (p = 0.016).
Conclusions: About one-fourth of patients had severe PPM and almost all of them had received a bioprosthesis. Sixty-month survival was significantly lower in patients with severe mismatch, or moderate mismatch with PH. Specifically, when a bioprothesis is chosen and while further evidence on the impact of PPM on clinical outcomes appears, surgeons are recommended to follow a preoperative strategy to implant a mitral prosthesis of adequate size in order to prevent PP
Influence of the Ion Coordination Number on Cation Exchange Reactions with Copper Telluride Nanocrystals
Cu2-xTe nanocubes were used as starting seeds to access metal telluride
nanocrystals by cation exchanges at room temperature. The coordination number
of the entering cations was found to play an important role in dictating the
reaction pathways. The exchanges with tetrahedrally coordinated cations (i.e.
with coordination number 4), such as Cd2+ or Hg2+, yielded monocrystalline CdTe
or HgTe nanocrystals with Cu2-xTe/CdTe or Cu2-xTe/HgTe Janus-like
heterostructures as intermediates. The formation of Janus-like architectures
was attributed to the high diffusion rate of the relatively small tetrahedrally
coordinated cations, which could rapidly diffuse in the Cu2-xTe NCs and
nucleate the CdTe (or HgTe) phase in a preferred region of the host structure.
Also, with both Cd2+ and Hg2+ ions the exchange led to wurtzite CdTe and HgTe
phases rather than the more stable zinc-blende ones, indicating that the anion
framework of the starting Cu2- xTe particles could be more easily deformed to
match the anion framework of the metastable wurtzite structures. As hexagonal
HgTe had never been reported to date, this represents another case of
metastable new phases that can only be accessed by cation exchange. On the
other hand, the exchanges involving octahedrally coordinated ions (i.e. with
coordination number 6), such as Pb2+ or Sn2+, yielded rock-salt polycrystalline
PbTe or SnTe nanocrystals with Cu2-xTe@PbTe or Cu2-xTe@SnTe core@shell
architectures at the early stages of the exchange process. In this case, the
octahedrally coordinated ions are probably too large to diffuse easily through
the Cu2-xTe structure: their limited diffusion rate restricts their initial
reaction to the surface of the nanocrystals, where cation exchange is initiated
unselectively, leading to core@shell architectures.Comment: 11 pages, 7 figures in J. Am. Chem. Soc, 13 May 201
Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections
We consider testing independence in group-wise selections with some
restrictions on combinations of choices. We present models for frequency data
of selections for which it is easy to perform conditional tests by Markov chain
Monte Carlo (MCMC) methods. When the restrictions on the combinations can be
described in terms of a Segre-Veronese configuration, an explicit form of a
Gr\"obner basis consisting of moves of degree two is readily available for
performing a Markov chain. We illustrate our setting with the National Center
Test for university entrance examinations in Japan. We also apply our method to
testing independence hypotheses involving genotypes at more than one locus or
haplotypes of alleles on the same chromosome.Comment: 25 pages, 5 figure
Likelihood Geometry
We study the critical points of monomial functions over an algebraic subset
of the probability simplex. The number of critical points on the Zariski
closure is a topological invariant of that embedded projective variety, known
as its maximum likelihood degree. We present an introduction to this theory and
its statistical motivations. Many favorite objects from combinatorial algebraic
geometry are featured: toric varieties, A-discriminants, hyperplane
arrangements, Grassmannians, and determinantal varieties. Several new results
are included, especially on the likelihood correspondence and its bidegree.
These notes were written for the second author's lectures at the CIME-CIRM
summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition
Efficient and exact sampling of simple graphs with given arbitrary degree sequence
Uniform sampling from graphical realizations of a given degree sequence is a
fundamental component in simulation-based measurements of network observables,
with applications ranging from epidemics, through social networks to Internet
modeling. Existing graph sampling methods are either link-swap based
(Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration
Model). Both types are ill-controlled, with typically unknown mixing times for
link-swap methods and uncontrolled rejections for the Configuration Model. Here
we propose an efficient, polynomial time algorithm that generates statistically
independent graph samples with a given, arbitrary, degree sequence. The
algorithm provides a weight associated with each sample, allowing the
observable to be measured either uniformly over the graph ensemble, or,
alternatively, with a desired distribution. Unlike other algorithms, this
method always produces a sample, without back-tracking or rejections. Using a
central limit theorem-based reasoning, we argue, that for large N, and for
degree sequences admitting many realizations, the sample weights are expected
to have a lognormal distribution. As examples, we apply our algorithm to
generate networks with degree sequences drawn from power-law distributions and
from binomial distributions.Comment: 8 pages, 3 figure
Two factor saturated designs: cycles, Gini index and state polytopes
In this paper we analyze and characterize the saturated fractions of two-factor designs under the simple effect model. Using Li et al.ear algebra, we define a criterion to check whether a given fraction is saturated or not. We also compute the number of saturated fractions, providing an alternative proof of the Cayley's formula. Finally we show how, given a list of saturated fractions, Gini indexes of their margins and the associated state polytopes could be used to classify them
An Operational Definition of a Statistically Meaningful Trend
Linear trend analysis of time series is standard procedure in many scientific disciplines. If the number of data is large, a trend may be statistically significant even if data are scattered far from the trend line. This study introduces and tests a quality criterion for time trends referred to as statistical meaningfulness, which is a stricter quality criterion for trends than high statistical significance. The time series is divided into intervals and interval mean values are calculated. Thereafter, r2 and p values are calculated from regressions concerning time and interval mean values. If r2≥0.65 at p≤0.05 in any of these regressions, then the trend is regarded as statistically meaningful. Out of ten investigated time series from different scientific disciplines, five displayed statistically meaningful trends. A Microsoft Excel application (add-in) was developed which can perform statistical meaningfulness tests and which may increase the operationality of the test. The presented method for distinguishing statistically meaningful trends should be reasonably uncomplicated for researchers with basic statistics skills and may thus be useful for determining which trends are worth analysing further, for instance with respect to causal factors. The method can also be used for determining which segments of a time trend may be particularly worthwhile to focus on
- …