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Tumor immunotherapies have shown promising antitumor effects, especially immune checkpoint inhibitors (ICIs). However, only 12.46% of the patients benefit from the ICIs, the rest of them shows limited effects on ICIs or even accelerates the tumor progression due to the lack of the immune cell infiltration and activation in the tumor microenvironment (TME). In this study, we administrated a combination of Toll-like receptor 9 (TLR9) agonist CpG ODN and Transforming growth factor-β2 (TGF-β2) antisense oligodeoxynucleotide TIO3 to mice intraperitoneally once every other day for a total of four injections, and the first injection was 24 h after LLC cell inoculation. We found that the combination induced the formation of TME toward the enrichment and activation of CD8

BackgroundFinding conservative T cell epitopes in the proteome of numerous variants of SARS-COV-2 is required to develop T cell activating SARS-COV-2 capable of inducing T cell responses against SARS-COV-2 variants.MethodsA computational workflow was performed to find HLA restricted CD8+ and CD4+ T cell epitopes among conserved amino acid sequences across the proteome of 474727 SARS-CoV-2 strains.ResultsA batch of covserved regions in the amino acid sequences were found in the proteome of the SARS-COV-2 strains. 2852 and 847 peptides were predicted to have high binding affinity to distint HLA class I and class II molecules. Among them, 1456 and 484 peptides are antigenic. 392 and 111 of the antigenic peptides were found in the conseved amino acid sequences. Among the antigenic-conserved peptides, 6 CD8+ T cell epitopes and 7 CD4+ T cell epitopes were identifed. The T cell epitopes could be presented to T cells by high-affinity HLA molecules which are encoded by the HLA alleles with high population coverage.ConclusionsThe T cell epitopes are conservative, antigenic and HLA presentable, and could be constructed into SARS-COV-2 vaccines for inducing protective T cell immunity against SARS-COV-2 and their variants.

Melanoma is one of the most aggressive skin cancers worldwide. Although there has been much effort toward improving treatment options over the past few years, there remains an urgent need for effective therapy. Immunotherapy combined with chemotherapy has shown great promise in clinical trials. Here, we studied the cooperative effects of the small molecule drug pimozide, which has a therapeutic effect in melanoma, and RNA interference (RNAi) targeting PD-1, an important immune checkpoint molecule involved in tumor immune escape. PD-1 siRNA was delivered by attenuated Salmonella to melanoma-bearing mice in combination with pimozide. Our results demonstrated that the combination therapy had the optimal therapeutic effect on melanoma. The mechanisms underlying the efficacy involved the induction of apoptosis and an enhanced immune response. This study suggests that immunotherapy based on PD-1 inhibition combined with anticancer drugs could be a promising clinical strategy for the treatment of melanoma.

Given a locally compact separable metric space E, a perfect transformation defined on E induces a Zadeh extension, which is a transformation from the space of all upper semicontinuous fuzzy sets defined on E to itself. Here, the latter space is equipped with the hit-or-miss topology. In this setting, each upper semicontinuous fuzzy set is identified with its hypograph, a closed subset in the product space of E and [0,1]. This approach does not require the relevant fuzzy sets to hold a compact support, and it also overcomes the drawback of the traditional level-set method. Further, it is proved that the Zadeh extension with this setting is continuous in the hit-or-miss topology; and dynamical properties of Zadeh extension regarding iteration have been explored.

The Choquet capacity T of a random closed set X on a metric space E is regarded as or related to a non-additive measure, an upper probability, a belief function, and in particular a counterpart of the distribution functions of ordinary random vectors. While the upper semicontinuity of T on the space of all closed subsets of E (hit-or-miss topology) is highly desired, T is not necessarily u.s.c. if E is not compact, e.g. E=R^n. For any locally compact separable metric space E, this controversial situation can be resolved in the probabilistic context by stereographically projecting X into the Alexandroff compactification E"~ of E with the ''north pole'' added to the projection. This leads to a random compact set X@? that is defined on the same probability space, takes values in a space homeomorphic to the space of X, and possesses an equivalent probability law. Particularly, the Choquet capacity T@? of X@? is u.s.c. on the space of all closed subsets of E"~. Further, consequences of the upper semicontinuity of T@? are explored, and a proof of the equivalence between the upper semicontinuity of T and continuity from above on F(E) is provided.

A product symbolic dynamical system (PSDS) is more complex than the ordinary symbolic dynamical systems (OSDS), serves as a universal system for compact and totally disconnected dynamical systems, and provides a moderate framework for characterizing orbit structures of general dynamical systems, in particular for non-expansive dynamical systems. This paper first explores fundamental properties of PSDS: although it shares some properties of OSDS such as dense periodic points and topological mixing, the PSDS holds other remarkable properties such as non-expansivity, uncountable periodic points and infinite entropy (the OSDS is expansive with countable periodic points and finite entropy). Then, a necessary and sufficient condition for the existence of invariant sets of shift (with respect to the PSDS) is established for the general dynamical systems, which generalizes the corresponding result on the invariant sets of shift (with respect to an OSDS) and provides useful tool for identifying more complicated invariant sets of the given dynamical systems. Moreover, a general characterization of subshifts is also established for the PSDS, which reveals the structures of all compact and totally disconnected dynamical systems.

For any dynamical system ( E , d , f ) , where E is Hausdorff locally compact second countable (HLCSC), let F (resp., 2 E ) denote the space of all closed subsets (resp., non-empty closed subsets) of E equipped with the hit-or-miss topology τ f . Both F and 2 E are again HLCSC ( F actually compact), thus metrizable. Let ρ be such a metric (three metrics available). The main purpose is to determine the conditions on f that ensure the continuity of the induced hyperspace maps 2 f : F → F and 2 f : 2 E → 2 E defined by 2 f ( F ) = f ( F ) . With this setting, the induced hyperspace systems ( F , ρ , 2 f ) and ( 2 E , ρ , 2 f ) are compact and locally compact dynamical systems, respectively. Consequently, dynamical properties, particularly metric related dynamical properties, of the given system ( E , d , f ) can be explored through these hyperspace systems. In contrast, when the Vietoris topology τ v is equipped on 2 E , the space of the induced hyperspace topological dynamical system ( 2 E , τ v , 2 f ) is not metrizable if E is not compact metrizable, e.g., E = R n , implying that metric related dynamical concepts cannot be defined for ( 2 E , τ v , 2 f ) . Moreover, two examples are provided to illustrate the advantages of the hit-or-miss topology as compared to the Vietoris topology.

The concepts of collective sensitivity and compact-type collective sensitivity are introduced as stronger conditions than the traditional sensitivity for dynamical systems and Hausdorff locally compact second countable (HLCSC) dynamical systems, respectively. It is proved that sensitivity of the induced hyperspace system defined on the space of non-empty compact subsets or non-empty finite subsets (Vietoris topology) is equivalent to the collective sensitivity of the original system; sensitivity of the induced hyperspace system defined on the space of all non-empty closed subsets (hit-or-miss topology) is equivalent to the compact-type collective sensitivity of the original HLCSC system. Moreover, relations between these two concepts and other dynamics concepts that describe chaos are investigated.

Adler, Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces, but Walters indicated that Bowen’s entropy is metric-dependent. We propose a new definition of topological entropy for continuous mappings on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required), investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and McAndrew and is metric-independent for metrizable spaces. Yet, it holds various basic properties of Adler, Konheim and McAndrew’s entropy, e.g., the entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same entropy, the entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new entropy coincides with Adler, Konheim and McAndrew’s entropy for compact systems.

Let (X, f) be a compact topological dynamical system. Assume that in X there exist pairwise disjoint closed subsets A1, A2, … , Ak satisfying f ( A i ) ⊇ ∪ j = 1 k A j , i = 1 , 2 , … , k . Under this assumption, the authors proved that (2X, 2f), which is the induced hyperspace topological dynamical system of (X, f), has at least one subsystem that is topologically semiconjugate to the symbolic dynamical system (Σ(k), σ). Further, the authors studied the properties of such subsystems and established two necessary and sufficient conditions as well as two sufficient conditions to determine which of these existing subsystems of (2X, 2f) are actually topologically conjugate to the symbolic dynamical system (Σ(k), σ).

Hyperspace dynamical system ( 2 E , 2 f ) induced by a given dynamical system ( E , f ) has been recently investigated regarding topological mixing, weak mixing and transitivity that characterize orbit structure. However, the Vietoris topology on 2 E employed in these studies is non-metrizable when E is not compact metrizable, e.g., E = R n . Consequently, metric related dynamical concepts of ( 2 E , 2 f ) such as sensitivity on initial conditions and metric-based entropy, could not even be defined. Moreover, a condition on ( 2 E , 2 f ) equivalent to the transitivity of ( E , f ) has not been established in the literature. On the other hand, Hausdorff locally compact second countable spaces (HLCSC) appear naturally in dynamics. When E is HLCSC, the hit-or-miss topology on 2 E is again HLCSC, thus metrizable. In this paper, the concepts of co-compact mixing, co-compact weak mixing and co-compact transitivity are introduced for dynamical systems. For any HLCSC system ( E , f ) , these three conditions on ( E , f ) are respectively equivalent to mixing, weak mixing and transitivity on ( 2 E , 2 f ) (hit-or-miss topology equipped). Other noticeable properties of co-compact mixing, co-compact weak mixing and co-compact transitivity such as invariants for topological conjugacy, as well as their relations to mixing, weak mixing and transitivity, are also explored.

Motivated by the problem of modeling of coarse data in statistics, we investigate in this paper topologies of the space of upper semicontinuous functions with values in the unit interval [0,1] to define rigorously the concept of random fuzzy closed sets. Unlike the case of the extended real line by Salinetti and Wets, we obtain a topological embedding of random fuzzy closed sets into the space of closed sets of a product space, from which Choquet theorem can be investigated rigorously. Precise topological and metric considerations as well as results of probability measures and special properties of capacity functionals for random u.s.c. functions are also given.

When the hit-or-miss topology is employed, the space of all closed subsets of a Hausdorff, locally compact and second countable space (HLCSC) is known to be Hausdorff, compact and second countable, thus metrizable. This paper investigates metrics on this space by using Alexandroff compactification technique, with a more general metrization procedure developed. A note concerning the necessity of the condition HLCSC on E is included. With the constructed metric, we investigate a hyperspace Birkhoff ergodic theorem to explore the connection between orbital behaviors of hyperspace dynamical systems and Choquet capacities of random closed sets. Moreover, relations between the hit-or-miss topology and other hyperspace topologies or metrics such as the Vietoris topology, Hausdorff metric and Hausdorff–Buseman metric are also given.

Embedding of a topological dynamical system into another is a weaker condition than topological conjugacy between the two topological dynamical systems. In 2000, under the assumption of e-expansive, compact and totally disconnected systems, Shigeo Akashi found a sufficient condition for embedding a topological dynamical system (X,. d, f) into a symbolic dynamical system. The purpose of this paper is to present and prove a necessary and sufficient condition that determines exactly which of the topological dynamical systems can be embedded into symbolic dynamical systems and which ones cannot be. Particularly, Shigeo Akashi's result becomes a special case of this new sufficient condition.

Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required). This is achieved through the consideration of co-compact covers of the space. The advantages of co-compact entropy include: (1) it does not require the space to be compact and, thus, generalizes Adler, Konheim and McAndrew’s topological entropy of continuous mappings on compact dynamical systems; and (2) it is an invariant of topological conjugation, compared to Bowen’s entropy, which is metric-dependent. Other properties of co-compact entropy are investigated, e.g., the co-compact entropy of a subsystem does not exceed that of the whole system. For the linear system, (R; f), defined by f(x) = 2x, the co-compact entropy is zero, while Bowen’s entropy for this system is at least log 2. More generally, it is found that co-compact entropy is a lower bound of Bowen’s entropies, and the proof of this result also generates the Lebesgue Covering Theorem to co-compact open covers of non-compact metric spaces.