We study a generalization of the advice complexity model of online computation in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms that are robust if the advice is adversarial, and efficient is the advice is foolproof. We focus on four well-studied online problems, namely ski rental, online bidding, bin packing and list update. For ski rental and online bidding, we show how to obtain algorithms that are Pareto-optimal with respect to the competitive ratios achieved, whereas for bin packing and list update, we give online algorithms with worst-case tradeoffs in their competitiveness, depending on whether the advice is trusted or adversarial. More importantly, we demonstrate how to prove lower bounds, within this model, on the tradeoff between the number of advice bits and the competitiveness of any online algorithm.

We consider the list update problem as defined in the seminal work on competitive analysis by Sleator and Tarjan [12]. In this problem, a sequence of requests, consisting of items to access in a linked list, is given. After an item is accessed it can be moved to any position forward in the list at no cost (free exchange), and, at any time, any two adjacent items can be swapped at a cost of 1 (paid exchange). The cost to access an item is its current position in the list. The goal is to dynamically rearrange the list so as to minimize the total cost (accrued from accesses and exchanges) over the request sequence. We show a lower bound of 12/11 on the worst-case ratio between the performance of an (offline) optimal algorithm that can only perform free exchanges and that of an (offline) optimal algorithm that can perform both paid and free exchanges. This answers an outstanding question that has been open since 1996 [10].

Stochastic dominance is a technique for evaluating the performance of online algorithms that provides an intuitive, yet powerful stochastic order between the compared algorithms. When there is a uniform distribution over the request sequences, this technique reduces to bijective analysis. These methods have been applied in problems such as paging, list update, bin colouring, routing in array mesh networks, and in connection with Bloom filters, and have often provided a clear separation between algorithms whose performance varies significantly in practice. Despite their appealing properties, the above techniques are quite stringent, in that a relation between online algorithms may be either too difficult to establish analytically, or worse, may not even exist. In this paper, we propose remedies to these shortcomings. Our objective is to make all online algorithms amenable to the techniques of stochastic dominance and bijective analysis. First, we establish sufficient conditions that allow us to prove the bijective optimality of a certain class of algorithms for a wide range of problems; we demonstrate this approach in the context of well-studied online problems such as weighted paging, reordering buffer management, and 2-server on the circle. Second, to account for situations in which two algorithms are incomparable or there is no clear optimum, we introduce the bijective ratio as a natural extension of (exact) bijective analysis. Our definition readily generalizes to stochastic dominance. This makes it possible to compare two arbitrary online algorithms for an arbitrary online problem. In addition, the bijective ratio is a generalization of the Max/Max ratio (due to Ben-David and Borodin), and allows for the incorporation of other useful techniques such as amortized analysis. We demonstrate the applicability of the bijective ratio to one of the fundamental online problems, namely the continuous k-server problem on metrics such as the line, the circle, and the star. Among other results, we show that the greedy algorithm attains bijective ratios of O(k) across these metrics.

In nature, search processes that use randomly oriented steps of different lengths have been observed at both the microscopic and the macroscopic scales. Physicists have analyzed in depth two such processes on grid topologies: Intermittent Search, which uses two step lengths, and Lévy Walk, which uses many. Taking a computational perspective, this paper considers the number of distinct step lengths k as a complexity measure of the considered process. Our goal is to understand what is the optimal achievable time needed to cover the whole terrain, for any given value of k. Attention is restricted to dimension one, since on higher dimensions, the simple random walk already displays a quasi linear cover time. We say X is a k -intermittent search on the one dimensional n-node cycle if there exists a probability distribution 𝐩 =(p_i)_i=1^k , and integers L_1,L_2,… , L_k , such that on each step X makes a jump ± L_i with probability p_i , where the direction of the jump ( + or −) is chosen independently with probability 1/2. When performing a jump of length L_i , the process consumes time L_i , and is only considered to visit the last point reached by the jump (and not any other intermediate nodes). This assumption is consistent with biological evidence, in which entities do not search while moving ballistically. We provide upper and lower bounds for the cover time achievable by k-intermittent searches for any integer k. In particular, we prove that in order to reduce the cover time (n^2) of a simple random walk to linear in n up to logarithmic factors, roughly log n/loglog n step lengths are both necessary and sufficient, and we provide an example where the lengths form an exponential sequence. In addition, inspired by the notion of intermittent search, we introduce the Walk or Probe problem, which can be defined with respect to arbitrary graphs. Here, it is assumed that querying (probing) a node takes significantly more time than moving to a random neighbor. Hence, to efficiently probe all nodes, the goal is to balance the time spent walking randomly and the time spent probing. We provide preliminary results for connected graphs and regular graphs.

AimsWe have shown that extracellular vesicles (EVs) secreted by embryonic stem cell-derived cardiovascular progenitor cells (Pg) recapitulate the therapeutic effects of their parent cells in a mouse model of chronic heart failure (CHF). Our objectives are to investigate whether EV released by more readily available cell sources are therapeutic, whether their effectiveness is influenced by the differentiation state of the secreting cell, and through which mechanisms they act.Methods and resultsThe total EV secreted by human induced pluripotent stem cell-derived cardiovascular progenitors (iPSC-Pg) and human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CM) were isolated by ultracentrifugation and characterized by Nanoparticle Tracking Analysis, western blot, and cryo-electron microscopy. In vitro bioactivity assays were used to evaluate their cellular effects. Cell and EV microRNA (miRNA) content were assessed by miRNA array. Myocardial infarction was induced in 199 nude mice. Three weeks later, mice with left ventricular ejection fraction (LVEF) ≤ 45% received transcutaneous echo-guided injections of iPSC-CM (1.4 × 106, n = 19), iPSC-Pg (1.4 × 106, n = 17), total EV secreted by 1.4 × 106 iPSC-Pg (n = 19), or phosphate-buffered saline (control, n = 17) into the peri-infarct myocardium. Seven weeks later, hearts were evaluated by echocardiography, histology, and gene expression profiling, blinded to treatment group. In vitro, EV were internalized by target cells, increased cell survival, cell proliferation, and endothelial cell migration in a dose-dependent manner and stimulated tube formation. Extracellular vesicles were rich in miRNAs and most of the 16 highly abundant, evolutionarily conserved miRNAs are associated with tissue-repair pathways. In vivo, EV outperformed cell injections, significantly improving cardiac function through decreased left ventricular volumes (left ventricular end systolic volume: -11%, P < 0.001; left ventricular end diastolic volume: -4%, P = 0.002), and increased LVEF (+14%, P < 0.0001) relative to baseline values. Gene profiling revealed that EV-treated hearts were enriched for tissue reparative pathways.ConclusionExtracellular vesicles secreted by iPSC-Pg are effective in the treatment of CHF, possibly, in part, through their specific miRNA signature and the associated stimulation of distinct cardioprotective pathways. The processing and regulatory advantages of EV could make them effective substitutes for cell transplantation.

We consider the setting of online computation with advice and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of 1 with only a constant number of bits of advice per request. For the bin packing problem, we give an online algorithm with advice that is (1+ε)-competitive and uses O(1εlog⁡1ε) bits of advice per request. For scheduling on m identical machines, with the objective function of any of makespan, machine covering and the minimization of the ℓp norm, p>1, we give similar results. We give online algorithms with advice which are (1+ε)-competitive ((1/(1−ε))-competitive for machine covering) and also use O(1εlog⁡1ε) bits of advice per request. We complement our results by giving a lower bound that shows that for any online algorithm with advice to be optimal, for any of the above scheduling problems, a non-constant number (namely, at least (1−2mn)log⁡m, where n is the number of jobs and m is the number of machines) of bits of advice per request is needed.

In the reordering buffer management problem, a sequence of colored items arrives at a service station to be processed. Each color change between two consecutively processed items generates some cost. A reordering buffer of capacity k items can be used to preprocess the input sequence in order to decrease the number of color changes. The goal is to find a scheduling strategy that, using the reordering buffer, minimizes the number of color changes in the given sequence of items. We consider the problem in the setting of online computation with advice. In this model, the color of an item becomes known only at the time when the item enters the reordering buffer. Additionally, together with each item entering the buffer, we get a fixed number of advice bits, which can be seen as information about the future or as information about an optimal solution (or an approximation thereof) for the whole input sequence. We show that for any \(\varepsilon > 0\) there is a \((1+\varepsilon )\)-competitive algorithm for the problem which uses only a constant (depending on \(\varepsilon \)) number of advice bits per input item. This also immediately implies a \((1+\varepsilon )\)-approximation algorithm which has \(2^{O(n\log 1/\varepsilon )}\) running time (this should be compared to the trivial optimal algorithm which has a running time of \(k^{O(n)}\)). We complement the above result by presenting a lower bound of \(\varOmega (\log k)\) bits of advice per request for any 1-competitive algorithm.

While randomized online algorithms have access to a sequence of uniform random bits, deterministic online algorithms with advice have access to a sequence of advice bits, i.e., bits that are set by an all powerful oracle prior to the processing of the request sequence. Advice bits are at least as helpful as random bits, but how helpful are they? In this work, we investigate the power of advice bits and random bits for online maximum bipartite matching (MBM). The well-known Karp-Vazirani-Vazirani algorithm is an optimal randomized $(1-\frac{1}{e})$-competitive algorithm for \textsc{MBM} that requires access to $\Theta(n \log n)$ uniform random bits. We show that $\Omega(\log(\frac{1}{\epsilon}) n)$ advice bits are necessary and $O(\frac{1}{\epsilon^5} n)$ sufficient in order to obtain a $(1-\epsilon)$-competitive deterministic advice algorithm. Furthermore, for a large natural class of deterministic advice algorithms, we prove that $\Omega(\log \log \log n)$ advice bits are required in order to improve on the $\frac{1}{2}$-competitiveness of the best deterministic online algorithm, while it is known that $O(\log n)$ bits are sufficient. Last, we give a randomized online algorithm that uses $c n$ random bits, for integers $c \ge 1$, and a competitive ratio that approaches $1-\frac{1}{e}$ very quickly as $c$ is increasing. For example if $c = 10$, then the difference between $1-\frac{1}{e}$ and the achieved competitive ratio is less than $0.0002$.

In this paper, we study the advice complexity of the online bin packing problem. In this well-studied setting, the online algorithm is supplemented with some additional information concerning the input. We improve upon both known upper and lower bounds of online algorithms for this problem. On the positive side, we first provide a relatively simple algorithm that achieves a competitive ratio arbitrarily close to 1.5, using constant-size advice. Our result implies that 16 bits of advice suffice to obtain a competitive ratio better than any online algorithm without advice, thus improving the previously known bound of O(log(n)) bits required to attain this performance. In addition, we introduce a more complex algorithm that still requires only constant-size advice, and has a competitive ratio arbitrarily close to 1.47012. This is the currently best performance of any online bin packing algorithm with sublinear advice. On the negative side, we extend a construction due to Boyar et al. (Algorithmica 74(1), 507–527 2016) so as to show that no online algorithm with sub-linear advice can be 7/6-competitive, improving on the lower bound of 9/8 from Boyar et al.

Les algorithmes en ligne fonctionnent dans un contexte ou l'entree est revele au fur et a mesure du temps; chaque morceau revele est appele une demande. Apres reception de chaque demahde, les algorithmes en ligne doivent prendre une action avant que la prochaine demande soit revelee, c'est-a-dire que les algorithmes en ligne doivent prendre une decision irrevocable basee sur les demandes deja revelees sans aucune connaissance des demandes a venir. Le but est d'optimiser une fonction de cout dependante de l'entree. L'analyse competitive est la methode standard utilisee pour analyser la qualite des algorithmes en ligne. Le ratio competitif est un ratio de pire cas, parmi toutes les sequences de demande finis, entre la performance de l'algorithme en ligne contre un algorithme optimal hors ligne pour la meme sequence. Le ratio competitif compare la performance d'un algorithme sans aucune connaissance de l'avenir contre un algorithme en pleine connaissance de l'avenir. Car l'absence totale de connaissance de l'avenir n'est souvent pas une hypothese raisonnable, des modeles ont ete proposes, appeles algorithmes en ligne avec conseil, qui donne les algorithmes en ligne l'acces a une quantite quantifiee des connaissances de l'avenir. L'interet de ce modele est d'examiner comment le ratio competitif change en fonction de la quantite de conseil. Dans cette these, il est presente des bornes superieures et inferieures dans ce modele pour des problemes en ligne classiques, tels que le probleme de la k-serveur, de bin packing, de dual bin packing (sac a dos multiple), d'ordonnancement sur m machines identiques, du tampon de reordonnancement et de la mise a jour de la liste.

Background and Aim: Our objective was to identify the molecular genetic basis of an Alagille-like condition not linked to JAG1 or NOTCH2 in two related sibships.Methods: Because of common ancestry, and an autosomal recessive mode of inheritance, it was hypothesized that all affected and no unaffected individuals would be homozygous for the same haplotype in the region of the causative gene. Single nucleotide polymorphism arrays were therefore used to genotype 3 affected individuals from two sibships, their mothers and four unaffected siblings, to identify regions of homozygosity. Genes within the largest regions were prioritized and sequenced for mutations. Mutant RNA transcripts were also sequenced.Results: A novel splice acceptor site mutation in the ATP8B1 gene was identified (a G-C preceding exon 16 resulting in a 4 bp deletion and frameshift from the 5' end of exon 16). This result was unexpected because ATP8B1 mutations are associated with Progressive Familial Intrahepatic Cholestasis Type 1 (PFIC1). Intrahepatic bile duct paucity, cardiac anomalies, renal tubular acidosis and hypothyroidism led to an initial diagnosis of Alagille Syndrome. However, in retrospect, abnormal sweat chloride, normal gamma-glutamyl transferase, normal to low cholesterol, and an autosomal recessive mode of inheritance were consistent with PFIC1. Renal tubular acidosis, hypothyroidism and cardiac anomalies have not previously been associated with PFIC1.Conclusion: This work expands the phenotypic spectrum of PFIC1, and highlights the overlap in clinical phenotype between Alagille Syndrome and PFIC1. Knowledge of the causative mutation allows for carrier testing and prenatal diagnosis in this community.

We consider the model of online computation with advice [5]. In particular, we study the k-server problem under this model. We prove two upper bounds for this problem. First, we show a ⌈⌈log k⌉/b-2⌉ -competitive online algorithm for general metric spaces with b bits of advice per request, where 3 ≤ b ≤ logk. This improves upon the recent result of [1]. Moreover, we believe that our algorithm and our analysis are more intuitive and simpler than those of [1]. Second, we give a 1-competitive online algorithm for trees which uses 2 + 2⌈log(p + 1)⌉ bits of advice per request, where p is the caterpillar dimension of the tree.

The gene dosage inequality between females with two X-chromosomes and males with one is compensated for by X-chromosome inactivation (XCI), which ensures the silencing of one X in every somatic cell of female mammals. XCI in humans results in a mosaic of two cell populations: those expressing the maternal X-chromosome and those expressing the paternal X-chromosome. We have previously shown that the degree of mosaicism (the X-inactivation pattern) in a Canadian family is directly related to disease severity in female carriers of the X-linked recessive bleeding disorder, haemophilia A. The distribution of X-inactivation patterns in this family was consistent with a genetic trait having a co-dominant mode of inheritance, suggesting that XCI choice may not be completely random. To identify genetic elements that could be responsible for biased XCI choice, a linkage analysis was undertaken using an approach tailored to accommodate the continuous nature of the X-inactivation pattern phenotype in the Canadian family. Several X-linked regions were identified, one of which overlaps with a region previously found to be linked to familial skewed XCI. SA2, a component of the cohesin complex is identified as a candidate gene that could participate in XCI through its association with CTCF.