A Framework for Adversarially Robust Streaming Algorithms

We investigate the adversarial robustness of streaming algorithms. In this context, an algorithm is considered robust if its performance guarantees hold even if the stream is chosen adaptively by an adversary that observes the outputs of the algorithm along the stream and can react in an online manner. While deterministic streaming algorithms are inherently robust, many central problems in the streaming literature do not admit sublinear-space deterministic algorithms; on the other hand, classical space-efficient randomized algorithms for these problems are generally not adversarially robust. This raises the natural question of whether there exist efficient adversarially robust (randomized) streaming algorithms for these problems.

MACH PRINCIPLE AND SPACE-TIME METRIC

There are five arguments in favor of the statement that the metric (the concepts of lengths, intervals, time intervals) is determined by the influences of the entire surrounding world on the properties of the observed objects: 1) logical consequences of recognizing the relational nature of classical space-time and describing interactions based on the concept of long-range, 2) sequential relational interpretation of the Feynman - Wheeler absorber theory, 3) comparison of electromagnetic radiation densities and “scattering” galaxies, 4) mathematicians changing the axiom of Archimedes, 5) keeping the ideas of “metaphysics of light”.

Heisenberg, Bohr, Robertson, and the Uncertainty Principle

From the outset, Heisenberg had resolved to eliminate classical space-time pictures involving particles and waves from the quantum mechanics of the atom. He had wanted to focus instead on the properties actually observed and recorded in laboratory experiments, such as the positions and intensities of spectral lines. Alone in Copenhagen in February 1927, he now pondered on the significance and meaning of such experimental observables. Feeling the need to introduce at least some form of ‘visualizability’, he asked himself some fundamental questions, such as: What do we actually mean when we talk about the position of an electron? He went on to discover the uncertainty principle: the product of the ‘uncertainties’ in certain pairs of variables—called complementary variables—such as position and momentum cannot be smaller than Planck’s constant h (now h / 4π‎).

WHY DOES THE STRUGGLE AROUND SRT CONTINUE TO THIS DAY?

The purpose of this article is not to criticize the theory of relativity, but to try to understand why, despite more than a century of dominance in physics, it is constantly criticized by physicists. In this paper, a thorough analysis of A. Einstein's theory of relativity is carried out. It relies on philosophical, physical-mathematical, logical-historical methods of investigation. It is shown that in SRT there is an error in the physical interpretation of the mathematical formalism of the Lorentz transformation (epistemological error). Therefore, the interpretation of the SRT phenomena contains logical contradictions and paradoxes. It is also shown that a consistent interpretation can be given for the Lorentz transformation within the framework of classical space-time representations. It is established that the real speed of the relative motion of inertial reference frames in is greater than the speed entering the Lorentz transformation. A new explanation is offered for relativistic phenomena without violating logic and without paradoxes. The results are of great importance for the description of relativistic phenomena in physical theories, and also for applied disciplines, for example, for the theory of cyclic accelerators, etc.

The Kalam Cosmological Argument

A survey of recent philosophical literature on the kalam cosmological argument reveals that arguments for the finitude of the past and, hence, the beginning of the universe remain robust. Plantinga’s brief criticisms of Kant’s argument in his First Antinomy concerning time are shown not to be problematic for the kalam argument. This chapter addresses, one by one, the two premises of the kalam, focusing on their philosophical aspects. The notion of infinity, both actual and potential, is discussed in relation to the coming into being of the universe. In addition, the scientific aspects of the two premises are also, briefly, addressed. Among these are the Borde-Guth-Vilenkin theorem, which proves that classical space-time cannot be extended to past infinity but must reach a boundary at some time in the finite past. This, among other factors, lends credence to the kalam argument’s second premise.