California State University, Los Angeles (Cal State LA) is a public university in Los Angeles, California. It is part of the 23-campus California State University (CSU) system. Cal State LA offers 142 bachelor's degrees, 122 master's degrees, and four doctoral degrees: a Doctor of Philosophy (Ph.D.) in special education in collaboration with the University of California, Los Angeles (UCLA), a Doctor of Education (Ed.D.) in Educational Leadership, a Doctor of Nursing Practice (DNP) and a Doctor of Audiology (AuD). It also offers 22 teaching credentials.In fall 2018, Cal State LA received the 5th-most applications of any CSU campus for incoming freshmen, and had the 4th-lowest admission rate. Cal State LA has a student body of 26,342 as of fall 2020, which includes 22,566 undergraduates, primarily from the greater Los Angeles area, and 3,776 graduate students. While Cal State LA previously operated on the quarter system, the university transitioned to the semester system starting in fall 2016, with each academic year now consisting of two 15-week semesters. Cal State LA is organized into nine colleges that house a total of four schools and approximately 50 academic departments, divisions and interdisciplinary programs, offering a variety of majors. The university’s forensic science program is one of the oldest in the nation. The Early Entrance Program (EEP) in the Honors College for gifted students as young as 12 is the only one of its kind in the United States in promoting a direct transitional scheme from middle and high school to college without intermediary remedial education. Cal State LA is a Hispanic-serving institution and is eligible to be designated as an Asian American Native American Pacific Islander serving institution (AANAPISI).The 175-acre (71 ha) hilltop campus core is home to the nation's first Charter College of Education, the Pat Brown Institute for Public Affairs, the Hertzberg-Davis Forensic Science Center, the Hydrogen Research and Fueling Facility and the Luckman Fine Arts Complex.It is also home to two high schools: the Marc and Eva Stern Math and Science School and the Los Angeles County High School for the Arts (LACHSA), the only arts high school in Los Angeles that allows students from any district within Los Angeles County to attend.D.D.
Native plant landscaping is gaining traction in cities worldwide for its potential to enhance biodiversity and ecosystem function. However, it remains unclear to what extent native plants increase animal-floral interactions compared to conventional landscaping such as lawns and ornamental plants. We quantified insect and bird flower visitation networks in 31 residential yards across Greater Los Angeles, California. We also assessed whether native plants in low-income areas, often lacking green amenities (the luxury effect), can support diverse floral-visitation networks. From April to September 2023, we conducted three visits each to 18 paired yards (one native-planted, one conventional) and 13 additional native-landscaped yards. We used timed area searches to quantify insect and bird floral visitation and collected predictor data on air quality, temperature, plant cover, species identity, flower color, phenology, as well as housing prices. Native-landscaped yards supported 4× higher floral-visitor abundance and 1.5× higher richness than conventional yards, largely driven by bees (Apidae) and hoverflies (Syrphidae), which were positively associated with native plant richness, flower-color diversity, and housing price. Several native plant species, including California buckwheat (Eriogonum fasciculatum) and white sage (Salvia apiana) anchored interaction networks. Moreover, native-landscaped yards contained 2.9× more interactions (140 vs. 48 edges) and exhibited higher network connectivity and redundancy. Floral visitors used native plants disproportionately, with native plants receiving 88
Giant reed (Arundo donax) has invaded biologically diverse riparian ecosystems in warm and arid regions globally, yet its impacts on wildlife are still poorly understood. Resolving the multi-taxa, scale-explicit impacts of giant reed in the broader context of the riparian vegetation mosaics that support wildlife can help target ecological restoration efforts. We quantified effects of giant reed and other dominant riparian vegetation on bird and butterfly habitat occupancies at two spatial scales along the Rio Grande in west Texas, USA. Birds and butterflies are diverse in riparian systems and can be efficiently surveyed, making them useful indicator taxa. We surveyed 167 sites three times per year in 2016 and 2017, and used occupancy models to relate occupancy to cover proportions of dominant vegetation types derived from high-resolution aerial imagery at two scales (100 m and 500 m radii) to assess local vs. broader floodplain-scale effects. Five of 16 bird species (31
In this paper, we focus on two types of degenerate partial differential equations: a degenerate elliptic equation and a degenerate parabolic equation. Significantly, both categories are characterized by the same principal operator. To obtain solutions for these equations, we introduce a novel approximation approach, termed the shape design approximation. As a practical application of this method, we derive a Carleman estimate for the backward degenerate parabolic equation. This estimate plays a pivotal role in establishing the null controllability of the degenerate parabolic equation. A notable advantage of employing the shape design approximation in deriving the Carleman estimate is that it enables us to bypass the requirement for second order derivatives in the degenerate equation. Usually, this has been a significant obstacle in the derivation of Carleman estimates for degenerate parabolic equations.
Our first main contribution consists in establishing an explicit formula of the critical mass via the best constant of the Gagliardo-Nirenberg inequality for the mixed local-nonlocal Laplacian. We also prove the existence of an optimizer of the Gagliardo-Nirenberg inequality for the mixed local-nonlocal operator. We then show that the optimizer (after some suitable scaling) is an energy ground state solution (with critical mass ). This is a key ingredient to determine sufficient and necessary conditions of existence and non-existence of energy ground state solutions in the in-between critical exponents case. Finally, we show that the energy ground state solution uc0 is an optimizer of the Gagliardo-Nirenberg inequality for the mixed local-nonlocal operator.
We introduce the notion of invariant vectors of a game and develop the Invariance Reduction Process, which first uses reduction of positions via invariance and then zero and merge reductions of games to arrive at smaller, solved sub-games for closed subspaces of the positions. This process makes it much easier to prove that there are moves from N-positions to P-positions, and can also be used in some cases to show that there are no moves between P-positions. This process is suitable for all variations of the game Nim whose rule sets form a simplicial complex. We rephrase Simplicial Nim as Set Nim SN(n,A) and derive results on the structure of the P-positions in terms of invariant vectors, without needing the background and notation of simplicial complexes. We also show that invariant vectors differ from the circuits used to describe the P-positions in Simplicial Nim and that invariant vectors have wider applicability compared to circuits. We apply the Invariance Reduction Process to derive results on the P-positions of the family of Path Nim games where play is allowed on at least half the stacks, as well as for the Circular Nim games CN(n,k) with n=7, k=3 and n=8,k=3.
