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We show that right-continuous monotone strategies used in Markov perfect equilibria for economic growth models and related dynamic games can be recognised as members of the Hilbert space of square integrable functions of the state variable. We provide an application of this result to a bequest game and point out that this result also holds for the class of left-continuous monotone functions. The result is fundamental for using the Schauder fixed point theorem. Furthermore, it considerably simplifies the classical approach, where such strategies are represented by non-negative measures on the state space.

We study Markov decision processes with Borel state spaces under quasi-hyperbolic discounting. This type of discounting nicely models human behaviour, which is time-inconsistent in the long run. The decision maker has preferences changing in time. Therefore, the standard approach based on the Bellman optimality principle fails. Within a dynamic game-theoretic framework, we prove the existence of randomised stationary Markov perfect equilibria for a large class of Markov decision processes with transitions having a density function. We also show that randomisation can be restricted to two actions in every state of the process. Moreover, we prove that under some conditions, this equilibrium can be replaced by a deterministic one. For models with countable state spaces, we establish the existence of deterministic Markov perfect equilibria. Many examples are given to illustrate our results, including a portfolio selection model with quasi-hyperbolic discounting.

In this paper, we consider constrained discounted stochastic games with a countably generated state space and norm continuous transition probability having a density function. We prove existence of approximate stationary equilibria and stationary weak correlated equilibria. Our results imply the existence of stationary Nash equilibrium in ARAT stochastic games.

Over the last decade, we have seen tremendous progress in research on 2-deoxy-D-glucose (2-DG) and its analogs. Clinical trials of 2-DG have demonstrated the challenges of using 2-DG as a monotherapy, due to its poor drug-like characteristics, leading researchers to focus on improving its bioavailability to tissue and organs. Novel 2-DG analogs such as WP1122 and others have revived the old concept of glycolysis inhibition as an effective anticancer strategy. Combined with other potent cytotoxic agents, inhibitors of glycolysis could synergistically eliminate cancer cells. We focused our efforts on the development of new combinations of anticancer agents coupled with 2-DG and its derivatives, targeting glioblastoma, which is in desperate need of novel approaches and therapeutic options and is particularly suited to glycolysis inhibition, due to its reliance on aerobic glycolysis. Herein, we present evidence that a combined treatment of 2-DG analogs and modulation of histone deacetylases (HDAC) activity via HDAC inhibitors (sodium butyrate and sodium valproate) exerts synergistic cytotoxic effects in glioblastoma U-87 and U-251 cells and represents a promising therapeutic strategy.

Our concerns have been raised about whether prolonged exposure to ammunition-related chemicals could correlate with genomic instability predisposing to lung carcinogenesis. The group of professional soldiers engaged in routine ammunition analysis and its explosive properties testing. To assess the presence of an innate genetic profile, DNA isolated from swabs was analyzed with LungCarta and HS Lung Panels and MassARRAY Analyzer 4 mass spectrometry. The presence of new somatic single nucleotide polymorphisms (SNPs) was detected with liquid biopsy technique and circulating cell-free DNA (ccfDNA) isolation, which was further analyzed with UltraSeek Lung Panel. Both genetic profiles obtained for each individual were compared. Genetic analysis revealed that in professional soldiers with long-term exposure to ammunition-related toxic chemicals, new SNPs in genes related to lung carcinogenesis are present. The preliminary data indicate that using modern molecular techniques could be a valuable tool for monitoring the genome instability in context of occupational risk of harmful volatile toxic compounds and improving personnel safety. The analyzed group will be further enlarged, and follow-up studies will be continued.

In this paper, we consider a stochastic economic growth model in the form of an intergenerational dynamic game. Both paternalistic and non-paternalistic components are present in the model. Under very general assumptions allowing for unbounded utility functions and weakly continuous transitions, we establish the existence of Markov perfect equilibria that consist of a consumption strategy and an indirect utility function. In the pure paternalistic case, we obtain new results on equilibria. An important point of our contribution is that we make no separability assumptions on the utility functions of generations.

In this paper, we investigate a Markov decision process with constraints on a Borel state space with the expected total reward criterion. Assuming that the transition probability has a density func...

This report presents a case of a 2-month-old female German Shepherd dog with renal nephroblastoma and strong cachexia. The tumour was surgically removed and graded as a stage I with favourable histopathology, but due to its large size, adjuvant chemotherapy, including doxorubicin and vincristine, was recommended. Before, during and after chemotherapy, the body weight was gradually rebuilt with an appropriately balanced diet containing proper amounts of protein, fat and numerous supplements necessary for growth and development. Eighteen months after diagnosis, the dog was in good condition and had no metastases. In conclusion, this case study shows that close cooperation between oncologists and nutritionists is crucial for successful oncological therapy, especially in a cachectic patient.

We study a discrete-time non-stationary decision model in which the preferences of the decision maker change over time and are described by quasi-hyperbolic discounting. A time-consistent optimal solution in this model corresponds with a Markov perfect equilibrium in a stochastic game with uncountable state space played by countably many short-lived players. We show that Markov perfect equilibria may be constructed using a generalized policy iteration algorithm. This method is in part inspired by the fundamental works of Mertens and Parthasarathy (in: Raghavan, Ferguson, Parthasarathy, Vrieze (eds) Stochastic games and related topics, Kluwer Academic Publishers, Dordrecht, 1991; in: Neyman, Sorin (eds) Stochastic games and applications, Academic Publishers, Dordrecht, 2003) devoted to subgame perfect equilibria in standard n-person discounted stochastic games. If the one-period utilities and transition probabilities are independent of time, we obtain on new existence results on stationary Markov perfect equilibria in the models with unbounded from above utilities.

In this note, we prove the existence of a Markov perfect equilibrium in a non-stationary version of a paternalistic bequest game. The method we advocate is general and allows to study models with unbounded state space and unbounded utility functions. We cover both, the stochastic and deterministic cases. We provide a characterization of the set of all Markov perfect equilibria by means of a set-valued recursive equation involving the best response operator. In the stationary case, we show that there exists a set of strategies that is invariant under the best response mapping.

Muscle cachexia is one of the most critical unmet medical needs. Identifying the molecular background of cancer-induced muscle loss revealed a promising possibility of new therapeutic targets and new drug development. In this review, we will define the signal transducer and activator of transcription 3 (STAT3) protein’s role in the tumor formation process and summarize the role of STAT3 in skeletal muscle cachexia. Finally, we will discuss a vast therapeutic potential for the STAT3-inhibiting single-agent treatment innovation that, as the desired outcome, could block tumor growth and generally prevent muscle cachexia.

In this paper, we study discounted stochastic games with Borel state and compact action spaces depending on the state variable. The primitives of our model satisfy standard continuity and measurability conditions. The transition probability is a convex combination of finitely many probability measures depending on states, and it is dominated by some finite measure on the state space. The coefficients of the combination depend on both states and action profiles. This class of models contains stochastic games with Borel state spaces and finite, state-dependent action sets. Our main result establishes the existence of subgame perfect equilibria, which are stationary in the sense that the equilibrium strategy for each player is determined by a single function of the current and previous states of the game. This dependence is called almost Markov. Our result enhances both the theorem of Mertens and Parthasarathy established in 1991 for games with finite, state-independent action sets, where the equilibrium strategies were also depended on the calendar time, and their result on stationary equilibria proved under an additional condition that the transition probabilities are atomless. A counterexample given very recently by Levy shows that stationary Markov perfect equilibria may not exist in the class of games considered in this paper. The presented results in this work are illustrated by the Cournot dynamic games, which were already considered in the literature under much stronger assumptions.

In this paper, we prove the existence of a stationary equilibrium in an intergenerational stochastic game with non-paternalistic altruism as defined by Ray (1987). Our approach is based on the assumption that the transition probabilities are non-atomic. The utility function of each generation has a very general form including many special cases studied in the literature.

Intensive exercise results in the increased blood concentration of the acute phase proteins in horses competing in some sport disciplines. In this study, the blood level of serum amyloid A (SAA) was analyzed in Thoroughbred racehorses during 5 days after completion of the race. Samples were collected from 25 healthy Thoroughbred horses beginning with 4 hours after the race and repeated daily up to the fifth day after the race. Serum amyloid A analysis was performed using commercial enzyme-linked immunosorbent assay kit, and the results were presented as median, interquartile range (IQR), and range. Data were analyzed using Friedman's nonparametric analysis of variance. The acute phase response (APR) was reflected by an increased SAA level after the race, reaching significantly higher concentrations on days 1 (P

The single-product, single-period newsvendor problem with two decision variables, namely price and stock quantity, is considered. The performance measure, in addition to the expected revenue, includes the variance of the income scaled with a risk parameter. We present conditions for the concavity of this risk-sensitive performance measure and the uniqueness of the optimal solution for both risk-averse and risk-seeking cases under the additive demand model, and compare the results to others previously published. These conditions are introduced in terms of the lost sales rate elasticity. Furthermore, we provide numerical examples that aim to endorse the theoretical results herein explained.

The ability of 2-deoxy-d-glucose (2-DG) to interfere with d-glucose metabolism demonstrates that nutrient and energy deprivation is an efficient tool to suppress cancer cell growth and survival. Acting as a d-glucose mimic, 2-DG inhibits glycolysis due to formation and intracellular accumulation of 2-deoxy-d-glucose-6-phosphate (2-DG6P), inhibiting the function of hexokinase and glucose-6-phosphate isomerase, and inducing cell death. In addition to glycolysis inhibition, other molecular processes are also affected by 2-DG. Attempts to improve 2-DG’s drug-like properties, its role as a potential adjuvant for other chemotherapeutics, and novel 2-DG analogs as promising new anticancer agents are discussed in this review.

We study discrete-time discounted constrained Markov decision processes (CMDPs) with Borel state and action spaces. These CMDPs satisfy either weak (W) continuity conditions, that is, the transition probability is weakly continuous and the reward function is upper semicontinuous in state–action pairs, or setwise (S) continuity conditions, that is, the transition probability is setwise continuous and the reward function is upper semicontinuous in actions. Our main goal is to study models with unbounded reward functions, which are often encountered in applications, e.g., in consumption/investment problems. We provide some general assumptions under which the optimization problems in CMDPs are solvable in the class of randomized stationary policies and in the class of chattering policies introduced in this paper. If the initial distribution and transition probabilities are atomless, then using a general “purification result” of Feinberg and Piunovskiy we show the existence of a deterministic (stationary) optimal policy. Our main results are illustrated by examples.

The existence of Markov perfect equilibria for a deterministic bequest game with bounded from below utility function was established independently by Bernheim and Ray [2] and Leininger [8] . The aim of this paper is to provide a simpler proof that, in contrast to [2] , [8] , also works for models with unbounded, e.g., isoelastic utility functions. Our approach employs the concept of strict single crossing property, introduced by Milgrom and Shannon in [10] , and includes supermodular functions as special cases.

In this paper, we prove the existence of a stationary Markov perfect equilibrium for a stochastic version of the bequest game. A novel feature in our approach is the fact that the transition probability need not be non-atomic and therefore, the deterministic production function is not excluded from consideration. Moreover, in addition to the common expected utility we also deal with a utility that takes into account an attitude of the generation towards risk.

We deal with discounted ARAT stochastic games on a Borel state space with finite action spaces and nonatomic transition probabilities. We prove the existence of pure Nash equilibria in stationary almost Markov strategies that depend only on the current and previous state of the game. Our proof is based on an existence theorem for correlated equilibria in stochastic games and some results on the integrals of set-valued mappings with respect to a probability measure depending on a parameter.

We examine the average minimax control problem on a general state space with an unbounded cost function. The controller is uncertain about his model in the sense that he deals with a range of alternative models as possibly true. The aim of this paper is to establish the optimality inequality and to provide a minimax strategy for the controller. A new feature in our approach is an application of a generalised Tauberian relation that, in turn, allows us to impose relatively weak assumptions.

In this paper we study a Markov decision model with quasi-hyperbolic discounting and transition probability function depending on an unknown parameter. Assuming that the set of parameters is finite, the sets of states and actions are Borel and the transition probabilities satisfy some additivity conditions and are atomless, we prove the existence of a non-randomised robust Markov perfect equilibrium.

In this paper, we study intergenerational stochastic games that can be viewed as a special class of overlapping generations models under uncertainty. Making use of the theorem of Dvoretzky, Wald and Wolfowitz [27] from the statistical decision theory, we obtain new results on stationary Markov perfect equilibria for the aforementioned games, with a general state space, satisfying rather mild continuity and compactness conditions. A novel feature of our approach is the fact that we consider risk averse generations in the sense that they aggregate partial utilities using an exponential function. As a byproduct, we also provide a new existence theorem for intergenerational stochastic game within the standard framework where the aggregator is linear. Our assumptions imposed on the transition probability and utility functions allow to embrace a pretty large class of intergenerational stochastic games analysed recently in macroeconomics. Finally, we formulate a set of assumptions under which the stochastic process induced by the stationary Markov perfect equilibrium possesses an invariant distribution.

We study an altruistic growth model with production uncertainty viewed as an intergenerational stochastic game. The existence of stationary Markov perfect equilibria is proved under general assumptions on utility functions for the generations and for non-atomic transition probabilities. This paper answers some issues that arose from the literature in the 1980s decade.

The present study is centered on molecular mechanisms of the cytoprotective effect of geranylgeraniol (GGOH) in skeletal muscle harmed by statin-associated myopathy (SAM). GGOH via autophagy induction was purportedly assumed to prevent skeletal muscle viability impaired by statins, atorvastatin (ATR) or simvastatin (SIM). The C2C12 cell line was used as the &lsquo, in vitro&rsquo, model of muscle cells at different stages of muscle formation, and the effect of ATR or SIM on the cell viability, protein expression and mitochondrial respiration were tested. Autophagy seems to be important for the differentiation of muscle cells, however, it did not participate in the observed GGOH cytoprotective effects. We showed that ATR- and SIM-dependent loss in cell viability was reversed by GGOH co-treatment, although GGOH did not reverse the ATR-induced drop in the cytochrome c oxidase protein expression level. It has been unambiguously revealed that the mitochondria of C2C12 cells are not sensitive to SIM, although ATR effectively inhibits mitochondrial respiration. GGOH restored proper mitochondria functioning. Apoptosis might, to some extent, explain the lower viability of statin-treated myotubes as the pan-caspase inhibitor, N-Benzyloxycarbonyl-Val-Ala-Asp(O-Me) fluoromethyl ketone (Z-VAD-FMK), partly reversed ATR- or SIM-induced cytotoxic effects, however, it does not do so in conjunction with caspase-3. It appears that the calpain inhibitor, N-Acetyl-L-leucyl-L-leucyl-L-norleucinal (ALLM), restored the viability that was reduced by ATR and SIM (p &lt, 0.001). GGOH prevents SAM, in part, as a consequence of a caspase-3 independent pathway, probably by calpain system inactivation.

We consider a discrete-time dividend payout problem with risk sensitive shareholders. It is assumed that they are equipped with a risk aversion coefficient and construct their discounted payoff with the help of the exponential premium principle. This leads to a risk adjusted discounted cash flow of dividends. Within such a framework not only the expected value of the dividends is taken into account but also their variability. Our approach is motivated by a remark in Gerber and Shiu (2004). We deal with the finite and infinite time horizon problems and prove that, even in this general setting, the optimal dividend policy is a band policy. We also show that the policy improvement algorithm can be used to obtain the optimal policy and the corresponding value function. Next, an explicit example is provided, in which the optimal policy is shown to be of a barrier type. Finally, we present some numerical studies and discuss the influence of the risk sensitive parameter on the optimal dividend policy.

This paper generalizes the classical discounted utility model introduced in Samuelson (Rev. Econ. Stud. 4:155–161, 1937) by replacing a constant discount rate with a function. The existence of recursive utilities and their constructions are based on Matkowski’s extension of the Banach Contraction Principle. The derived utilities go beyond the class of recursive utilities studied in the literature and enable a discussion on subtle issues concerning time preferences in the theory of finance, economics or psychology. Moreover, our main results are applied to the theory of optimal economic growth related with resource extraction models with unbounded utility function of consumption.

In this paper, we study discounted Markov decision processes on an uncountable state space. We allow a utility (reward) function to be unbounded both from above and below. A new feature in our approach is an easily verifiable rate of growth condition introduced for a positive part of the utility function. This assumption, in turn, enables us to prove the convergence of a value iteration algorithm to a solution to the Bellman equation. Moreover, by virtue of the optimality equation we show the existence of an optimal stationary policy.

We study a discounted maxmin control problem with general state space. The controller is unsure about his model in the sense that he also considers a class of approximate models as possibly true. The objective is to choose a maxmin strategy that will work under a range of different model specifications. This is done by dynamic programming techniques. Under relatively weak conditions, we show that there is a solution to the optimality equation for the maxmin control problem as well as an optimal strategy for the controller. These results are applied to the theory of optimal growth and the Hansen–Sargent robust control model in macroeconomics. We also study a class of zero-sum discounted stochastic games with unbounded payoffs and simultaneous moves and give a brief overview of recent results on stochastic games with weakly continuous transitions and the limiting average payoffs.

In this note we study a deterministic dynamic programming model with generalised discounting. We use a modified weighted norm approach and an approximation technique to a study of the Bellman equation for unbounded return functions. Furthermore, we apply this theory to economic growth models.

Three-disulfide-bridged Ecballium elaterium trypsin inhibitor II (EETI-II) is a 28-residue peptide that belongs to the squash family of canonical trypsin inhibitors. Herein, we report synthesis and biological activity of three EETI-II analogs. In each of analog, a pair of cysteine residues forming a native disulfide bridge was individually replaced by a pair of selenocysteine residues. All selenopeptide analogs were chemically synthesized using the Fmoc protocol and subsequently folded in the presence of oxidized and reduced glutathione. The analogs containing a diselenide bridge displayed association constants with trypsin that ranged from 2.6 x 10(9) to 5.1 x 10(9) [M(-1) ]. Our results suggest that the selenopeptide analogs retained low nanomolar inhibitory potencies, and only the diselenide bridge adjacent to the inhibitory binding loop weakened the interactions with trypsin by approximately fivefold. We discuss these findings in the context of a broader use of selenopeptide analogs as proxies to study cysteine-rich peptides.

In this note, we study the Bellman-Poisson equation associated with a class of ergodic zero-sum semi-Markov games. The main objective is to prove that this equation has a continuous solution and both players have optimal stationary strategies.

Four 28-amino acid peptides were synthesized whose sequences comprised two molecules of trypsin inhibitor sunflower trypsin inhibitor 1 (SFTI-1) bound through a peptide bond. The peptides in their reactive positions (5 and 19 of the peptide chain) contain two Lys ([KK]BiSFTI-1) and two Phe ([FF]BiSFTI-1) residues, along with a combination of the amino acid residues named thereafter [KF]BiSFTI-1 and [FK]BiSFTI-1. Association constants of the analogues determined with trypsin and chymotrypsin, respectively, indicated that they were potent inhibitors of cognate proteinases. An MS study of the associates revealed that incubation of the compounds with the proteinases resulted in cutting out a fragment of the peptide chain to restore the native monocyclic molecule of SFTI-1 or its analogue [Phe5]SFTI-1. This process, analogous to that of the DNA and protein splicing, can be referred to as ‘peptide splicing’.

Zero-sum ergodic semi-Markov games with weakly continuous transition probabilities and lower semicontinuous, possibly unbounded, payoff functions are studied. Two payoff criteria are considered: the ratio average and the time average. The main result concerns the existence of a lower semicontinuous solution to the optimality equation and its proof is based on a fixed-point argument. Moreover, it is shown that the ratio average as well as the time average payoff stochastic games have the same value. In addition, one player possesses an e-optimal stationary strategy (e>0), whereas the other has an optimal stationary strategy.

Combinatorial chemistry approach was applied to design chromogenic substrates of human beta-tryptase. The most active substrate, Ala-Ala-Pro-Ile-Arg-Asn-Lys-ANB-NH(2), was selected from among over 9 million heptapeptides. The amide of 5-amino-2-nitrobenzoic acid (ANB-NH(2)) attached at the C-terminus served as a chromophore. In order to determine the optimal length of the tryptase substrate, a series of N-terminally truncated fragments of this substrate was synthesized. Pro-Ile-Arg-Asn-Lys-ANB-NH(2), with the determined value of the specificity constant (k(cat)/K(M)) above 9 x 10(6) M(-1) s(-1), appeared to be the most specific substrate of tryptase. This substrate was twice as active as the parent heptapeptide substrate. We postulate that the optimal size of the pentapeptide substrate for the interaction with human beta-tryptase is associated with the unique structure of this proteinase, comprising four almost identical monomer subunits arranged in a square flat ring with its substrate pockets faced inside, forming a tetramer with a central pore that can be penetrated by this short peptide.

A series of linear and monocyclic analogues of trypsin inhibitor SFTI-1 isolated from sunflower seeds, modified by N-(4-aminobutyl)glycine (Nlys) and N-benzylglycine (Nphe), were obtained by the solid-phase method. Some of these peptomers displayed trypsin or chymotrypsin inhibitory activity. In contradiction to the literature data, in most analogues peptide bonds formed by these peptoid monomers were at least partially hydrolyzed by the experimental enzymes at two different pH (3.5 and 8.3). Nevertheless, the replacement of Phe present in the P(1) substrate specificity of linear inactive SFTI-1 analogue with Nphe, yielded a potent chymotrypsin inhibitor. The introduction of one cyclic element (a disulfide bridge or head-to-tail cyclization) to the analogues synthesized significantly increased their proteinase resistance.