This is a straightforward generalization of the k-mean problem where the input is a set of n points instead of lines. We suggest the first PTAS that computes a (1 + ε)-approximation to this problem in time O(n log n) for any constant approximation error ε (0, 1), and constant integers k, d 1.

Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as decision trees and matrix factorizations. We suggest an algorithm that gets a finite set of n d-dimensional real vectors and returns a weighted subset of d + 1 vectors whose sum is exactly the same. The proof in Caratheodory's Theorem (1907) computes such a subset in O(n

Google's health and data company, Verily, is closing its operations in Israel three years after opening a research and development center in the country. Verily staff in Israel are expected to leave by the third quarter of 2024. The company cited an effort to refocus its strategy on core products and projects as the reason for the closure. "As part of our ongoing review of business needs, Verily has made the difficult decision to begin the process to close its R&D center in Israel located in both Haifa and Tel Aviv," a spokesperson for Verily said. "This decision is in keeping with our strategy as we continue to streamline our overall company operations."

Yemen's Houthis have claimed carrying out a joint military operation with an Iranian-backed Iraqi militia, known as the Islamic Resistance in Iraq, to target four vessels in Israel's Haifa port. Houthi military spokesman Yahya Saree said in a televised statement on Sunday that the group fired drones at two cement tankers and two cargo ships at the port a day prior over noncompliance with a ban on entering "ports of occupied Palestine". Saree added that the group had also targeted a Shorthorn Express ship in the Mediterranean Sea using drones, and both operations "successfully achieved their goals". Israel's Channel 12 reported an explosion occurred in Haifa at dawn after an air defence missile was launched towards the sea without activating the sirens. Israel's military did not comment on the Houthi claim, but stated in a post on X that it had shot down a drone approaching the country overnight from the east.

Israel is ready for an "all-out war" in Lebanon and has plans approved for an offensive targeting Hezbollah, officials have said. The claims from Israel's foreign minister and military late on Tuesday followed Hezbollah's release of threatening drone footage. The climbing tension conflicts with United States efforts to avert an escalation amid months of low-level hostilities across the Israel-Lebanon border. The nine-minute drone footage of the Israeli port city of Haifa filmed in daytime, showed civilian and military areas, including malls and residential quarters, in addition to a weapons manufacturing complex and missile defence batteries. Israel's Foreign Minister Israel Katz responded vehemently in a post on X, calling out Hezbollah chief Hassan Nasrallah for boasting about filming the ports of Haifa, which are operated by foreign companies from China and India.

Hezbollah has released drone footage that it claims shows the group's surveillance of Israel's port city of Haifa and its surroundings. The video includes aerial views of sites in Haifa including sea and airports.

Bandit Convex Optimization (BCO) is a fundamental framework for decision making under uncertainty, which generalizes many problems from the realm of online and statistical learning. While the special case of linear cost functions is well understood, a gap on the attainable regret for BCO with nonlinear losses remains an important open question. In this paper we take a step towards understanding the best attainable regret bounds for BCO: we give an efficient and near-optimal regret algorithm for BCO with strongly-convex and smooth loss functions. In contrast to previous works on BCO that use time invariant exploration schemes, our method employs an exploration scheme that shrinks with time.

The framework of online learning with memory naturally captures learning problems with temporal effects, and was previously studied for the experts setting. In this work we extend the notion of learning with memory to the general Online Convex Optimization (OCO) framework, and present two algorithms that attain low regret. The first algorithm applies to Lipschitz continuous loss functions, obtaining optimal regret bounds for both convex and strongly convex losses. The second algorithm attains the optimal regret bounds and applies more broadly to convex losses without requiring Lipschitz continuity, yet is more complicated to implement. We complement the theoretical results with two applications: statistical arbitrage in finance, and multi-step ahead prediction in statistics.

This document describes the rationale, the implementation and a preliminary evaluation of a semantic reasoning tool developed in the EU H2020 SPICE project to enhance the diversity of perspectives experienced by museum visitors. The tool, called DEGARI 2.0 for values, relies on the commonsense reasoning framework TCL, and exploits an ontological model formalizingthe Haidt's theory of moral values to associate museum items with combined values and emotions. Within a museum exhibition, this tool can suggest cultural items that are associated not only with the values of already experienced or preferred objects, but also with novel items with different value stances, opening the visit experience to more inclusive interpretations of cultural content. The system has been preliminarily tested, in the context of the SPICE project, on the collection of the Hecht Museum of Haifa.

This survey paper is an expanded version of an invited keynote at the ThEdu'22 workshop, August 2022, in Haifa (Israel). After a short introduction on the developments of CAS, DGS and other useful technologies, we show implications in Mathematics Education, and in the broader frame of STEAM Education. In particular, we discuss the transformation of Mathematics Education into exploration-discovery-conjecture-proof scheme, avoiding usage as a black box . This scheme fits well into the so-called 4 C's of 21st Century Education. Communication and Collaboration are emphasized not only between humans, but also between machines, and between man and machine. Specific characteristics of the outputs enhance the need of Critical Thinking. The usage of automated commands for exploration and discovery is discussed, with mention of limitations where they exist. We illustrate the topic with examples from parametric integrals (describing a "cognitive neighborhood" of a mathematical notion), plane geometry, and the study of plane curves (envelopes, isoptic curves). Some of the examples are fully worked out, others are explained and references are given.