Convex optimization framework for intermediate deadline assignment in soft and hard real-time distributed systems

It is generally challenging to determine end-to-end delays of applications for maximizing the aggregate system utility subject to timing constraints. Many practical approaches suggest the use of intermediate deadline of tasks in order to control and upper-bound their end-to-end delays. This paper proposes a unified framework for different time-sensitive, global optimization problems, and solves them in a distributed manner using Lagrangian duality. The framework uses global viewpoints to assign intermediate deadlines, taking resource contention among tasks into consideration. For soft real-time tasks, the proposed framework effectively addresses the deadline assignment problem while maximizing the aggregate quality of service. For hard real-time tasks, we show that existing heuristic solutions to the deadline assignment problem can be incorporated into the proposed framework, enriching their mathematical interpretation.

Convex and toric geometry to analyze complex dynamics in chemical reaction systems

Convex cone, toric variety, graph theory, electrochemical catalysis, oxidation of formic acid, feedback-loopsbifurcations, enzymatic catalysis, Peroxidase reaction, Shil'nikov chaos

Adelic convex geometry of numbers

Magdeburg, Univ., Fak. für Mathematik, Diss., 2014

Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

Permutations defining convex permutominoes

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Physa Marmorata Guilding, 1828 (Pulmonata: Physidae)

A description of Physa marmorata Guilding, 1828, based on material collected at its type-locality, the Caribbean island of Saint Vincent, is presented. The shell is thin, horn-colored, surface very glossy, diaphanous. Spire acute, elevated; protoconch distinct, rounded-conical, reddish-brown; five not shouldered, broadly convex whorls with subobsolete spiral lines and thin growth lines. Aperture elongated, 1.4-2.0 times as long as the remaining shell length, narrow obovate-lunate; upper half acute-angled,lower half oval,narrowly rounded at the base, outer lip sharp, inner lip completely closing the umbilical region; a very distinct callus on the parietal wall; columellar lip with a low ridge gradually merging into the callus. ratios: shell width/shell length = 0.44 - 0.52 (mean 0.47); spire length /shell lenght = 0.33-0.41 (mean 0.39); aperture length/shell lenght = 0.59-0.67 (mean 0.62). Oral lappets laterally mucronate, foot spatulate with deeply pigmented acuminate tail. Mantle reflection with 6-10 short triangular dentations covering nearly half the right surface of the body whorl, and 4-6 covering a part of the ventral wall. Body surface with tiny dots of greenish-yellow pigment besides melanin. Renal tube tightly folded in toa zigzag course. Ovotestis diverticula acinous, laterally pressed against each other around a collecting canal. Ovispermiduct with well-developed seminal vesicle. oviduct highly convoluted, merging into a less convoluted nidamental gland which narrows to a funnel-shaped uterus and a short vagina. Spermathecal body oblong, more or less constricted in the middle and somewhat curved; spermathecal duct uniformly narrow, a little longer than be body. About 20 prostatic diverticula, simple, bifurcate or divided into a few short branches, distalmost ones assembled into a cluster. Penis long, nearly uniformly narrow; penial canal with lateral opening about the junction of its middle and lower thirds. Penial sheath with a bulbous terminal expasion the tip of which isinserted into the caudal end of the prepuce. Prepuce shouldered, much wider than the narrow portion of the penial sheath. Penial sheath/prepuce ratio about 2.08 (1.45-2.75). The main extrinsic muscles of the penial complex are a retractor, with a branch attached to the bulb, and another to the caudal end of the penial sheath; and a protractor, with a branch attached to the shoulder of the prepuce and adjoining area of the penial sheath, and another to the caudal end of the penial sheath. Egg capsule C-shaped, with 10-30 elliptical eggs (snails 10mm long) measuring about 1.10 mm (0.90-1.32) through the long axis and surrounded by an inner and an outer lamellate membranes. Jaw a simple obtusely V-shaped plate. radula will be described separately.

Physa cubensis Pfeiffer, 1839 (Pulmonata: Physidae)

A description of Physa cubensis Pfeiffer, 1839, based on 15 speciments collected in Havana, Cuba, is presented. The shell, measuring 9.0 x 4,8mm to 12.3 x 6.4mm, is ovate-oblong, thin, diaphanous, horncolored, shining. Spire elevated, broadly conical; protoconch distinct, roundish, reddish-brown. About five moderately shouldered, roundly convex whorls, penultimate whorl expanded; spiral striation subobsolete; growth line faint on the intermediate whorls, clearly visible on the body whorl, crowded here and there. Suture well impressed. Aperture elongated 2.05 - 2.67 (mean 2.27) times as long as the remaining length of the shell, narrow obovulate-lunate; upper half acute-angled, lower half oval, narrowly rounded at the base; outer lip sharp, inner lip completely closing the umbilical region; a thick callus on the parietal wall; columellar plait well marked. Ratios: shell width/shell length - 0.52-0.61 (mean 0.55); spire length/shell length = 0.27 - 0.33 (mean 0.31); aperture length/shell length = 0.67 - 0.73 (mean 0.69). Oral lappets laterally mucronate; foot spatulate with acuminate tail. Mantle relection with 6 - 8 short triangular dentations in the right lobe (columellar side) and 4 - 6 in the left lobe (near the pneumostome). Renal tube tightly folded into a zigzag course. Ovotestis, ovispermiduct, seminal vesicle, oviduct, nidamental gland, uterus and vagina as in Physa marmorata (see Paraense, 1986, Mem. Inst. Oswaldo Cruz, 81: 459-469). Spermathecal body egg-shaped or pear-shaped; spermathecal ducta uniformly narrow with expanded base, a little longer than the body. Spermiduct, prostate and vas deferens as in P. marmorata (Paraense, loc. cit.). Penis wide proximally, narrowing gradually apicad; penial canal with subterminal outlet. Penial sheath following the width of the penis and ending up by a bulbous expansion somewhat narrower than the proximal portion. Penaial sheath/prepuce ration = 1,25 - 1,83 (mean 1.49). Prepuce much wider than the bulb of the penial shealth, moderately shouldered owing to the intromission of the bulb, and with a large gland in one side of its proximal half occupating about a third of its length. Extrinsic muscles of the penial complex as in P. marmorata. Jaw a simple obtusely V-shaped plate. Radula to be described separetely.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

On stability of solutions to systems of convex inequalities

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COMMIT: Convex Optimization Modeling for Microstructure Informed Tractography.

Tractography is a class of algorithms aiming at in vivo mapping the major neuronal pathways in the white matter from diffusion magnetic resonance imaging (MRI) data. These techniques offer a powerful tool to noninvasively investigate at the macroscopic scale the architecture of the neuronal connections of the brain. However, unfortunately, the reconstructions recovered with existing tractography algorithms are not really quantitative even though diffusion MRI is a quantitative modality by nature. As a matter of fact, several techniques have been proposed in recent years to estimate, at the voxel level, intrinsic microstructural features of the tissue, such as axonal density and diameter, by using multicompartment models. In this paper, we present a novel framework to reestablish the link between tractography and tissue microstructure. Starting from an input set of candidate fiber-tracts, which are estimated from the data using standard fiber-tracking techniques, we model the diffusion MRI signal in each voxel of the image as a linear combination of the restricted and hindered contributions generated in every location of the brain by these candidate tracts. Then, we seek for the global weight of each of them, i.e., the effective contribution or volume, such that they globally fit the measured signal at best. We demonstrate that these weights can be easily recovered by solving a global convex optimization problem and using efficient algorithms. The effectiveness of our approach has been evaluated both on a realistic phantom with known ground-truth and in vivo brain data. Results clearly demonstrate the benefits of the proposed formulation, opening new perspectives for a more quantitative and biologically plausible assessment of the structural connectivity of the brain.

Convex linear combination processes for compositions

Aitchison and Bacon-Shone (1999) considered convex linear combinations ofcompositions. In other words, they investigated compositions of compositions, wherethe mixing composition follows a logistic Normal distribution (or a perturbationprocess) and the compositions being mixed follow a logistic Normal distribution. Inthis paper, I investigate the extension to situations where the mixing compositionvaries with a number of dimensions. Examples would be where the mixingproportions vary with time or distance or a combination of the two. Practicalsituations include a river where the mixing proportions vary along the river, or acrossa lake and possibly with a time trend. This is illustrated with a dataset similar to thatused in the Aitchison and Bacon-Shone paper, which looked at how pollution in aloch depended on the pollution in the three rivers that feed the loch. Here, I explicitlymodel the variation in the linear combination across the loch, assuming that the meanof the logistic Normal distribution depends on the river flows and relative distancefrom the source origins

Refinement criteria for global illumination using convex funcions

In several computer graphics areas, a refinement criterion is often needed to decide whether to goon or to stop sampling a signal. When the sampled values are homogeneous enough, we assume thatthey represent the signal fairly well and we do not need further refinement, otherwise more samples arerequired, possibly with adaptive subdivision of the domain. For this purpose, a criterion which is verysensitive to variability is necessary. In this paper, we present a family of discrimination measures, thef-divergences, meeting this requirement. These convex functions have been well studied and successfullyapplied to image processing and several areas of engineering. Two applications to global illuminationare shown: oracles for hierarchical radiosity and criteria for adaptive refinement in ray-tracing. Weobtain significantly better results than with classic criteria, showing that f-divergences are worth furtherinvestigation in computer graphics. Also a discrimination measure based on entropy of the samples forrefinement in ray-tracing is introduced. The recursive decomposition of entropy provides us with a naturalmethod to deal with the adaptive subdivision of the sampling region

A convex optimization framework for global tractography

In this article we present a novel approach for diffusion MRI global tractography. Our formulation models the signal in each voxel as a linear combination of fiber-tract basis func- tions, which consist of a comprehensive set of plausible fiber tracts that are locally compatible with the measured MR signal. This large dictionary of candidate fibers is directly estimated from the data and, subsequently, efficient convex optimization techniques are used for recovering the smallest subset globally best fitting the measured signal. Experimen- tal results conducted on a realistic phantom demonstrate that our approach significantly reduces the computational cost of global tractography while still attaining a reconstruction quality at least as good as the state-of-the-art global methods.

Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.